Help with a maths question please!!

Atlas26

In preparation for Maths Paper 2 HL on Monday I decided to look over my mock paper. I was hoping someone here could help
The question reads:

The diagram shows a ladder leaning against a vertical wall. The ladder stands on horizontal ground.

The length of the ladder is 225cm

The ladder is safe to use when the angle marked y is 75°

(A) Is the ladder safe to use when it is 70cm from the base of the house? Justify your answer.
(B) What is the height the ladder can reach up the wall when it is in a safe position?

Would anyone be able to come with a method of doing this??

JIdontknow

Atlas26 wrote: »

In preparation for Maths Paper 2 HL on Monday I decided to look over my mock paper. I was hoping someone here could help
The question reads:

The diagram shows a ladder leaning against a vertical wall. The ladder stands on horizontal ground.

The length of the ladder is 225cm

The ladder is safe to use when the angle marked y is 75°

(A) Is the ladder safe to use when it is 70cm from the base of the house? Justify your answer.
(B) What is the height the ladder can reach up the wall when it is in a safe position?

Would anyone be able to come with a method of doing this??

Basically create a right angled triangle. The hypotenuse is 225, and the distance from the bottom of the ladder to the wall is 70cm. Then use sine rule to calculate, first use pythagerous 70 squared plus x squared = 225 squared.

Then use sine rule a/sine a = b /sine b.

I'm only on phone but create right angle triangle with the 225 the hyp, and 70 the base, so 70 across the bottom and the 225 diagonally opposite the 90 degree, pythagerous will calculate the remaining distance approx 213.8, this is the vertical height from base of right angle up (wall). Then use sine rule and you'll get an angle of 71.88 degrees, which is more than 70 degrees.

JIdontknow

JIdontknow wrote: »

Basically create a right angled triangle. The hypotenuse is 225, and the distance from the bottom of the ladder to the wall is 70cm. Then use sine rule to calculate, first use pythagerous 70 squared plus x squared = 225 squared.

Then use sine rule a/sine a = b /sine b.

I'm only on phone but create right angle triangle with the 225 the hyp, and 70 the base, so 70 across the bottom and the 225 diagonally opposite the 90 degree, pythagerous will calculate the remaining distance approx 213.8, this is the vertical height from base of right angle up (wall). Then use sine rule and you'll get an angle of 71.88 degrees, which is more than 70 degrees.

Then for the other part instead of the 70, you work from the angles instead, you have 70 degrees so other angle is 20 degrees, you've the length of the ladder (225) so you can use sine rule.

Atlas26

JIdontknow wrote: »

Basically create a right angled triangle. The hypotenuse is 225, and the distance from the bottom of the ladder to the wall is 70cm. Then use sine rule to calculate, first use pythagerous 70 squared plus x squared = 225 squared.

Then use sine rule a/sine a = b /sine b.

Ok, I've done the first part:
For the opposite side (x) I got 213.834 using Pythagoras's theorem. I don't understand what you mean by sine rule though...

JIdontknow

Atlas26 wrote: »

Ok, I've done the first part:
For the adjacent side (x) I got 213.834 using Pythagoras's theorem. I don't understand what you mean by sine rule though...

Not sure if ye have covered it yet ( don't know the syllabus) but sine rule is

a / sine a = b / sine b,

Apologies it's been years since I did it!

theLuggage

Sine Rule is not on JC course. You need to think about your SOHCAHTOA ratios, by which I mean Sin A = opp/hyp, Cos A = adj/hyp and Tan A = opp/adj.

I'm assuming the angle y is on the ground. If it's in the air then let me know because the following will change:

For this question part a the sides you have are the hypotenuse which is 225, and the adjacent which you are assuming to be 70. You need to use the Cos ratio to check if the angle works out to be 75 degrees. If it is then the ladder is safe at 70cm distance. If not, then it's not.

For part b, you are looking for the height of the wall which is the opposite side. So use Sin ration with 75 degree angle you have on the ground.

If the angle 75 deg is in the air, then part a will be the Sin ratio and for part b you would use the Cos ratio.

Hope this helps, and good luck!

Atlas26

theLuggage wrote: »

Sine Rule is not on JC course. You need to think about your SOHCAHTOA ratios, by which I mean Sin A = opp/hyp, Cos A = adj/hyp and Tan A = opp/adj.

I'm assuming the angle y is on the ground. If it's in the air then let me know because the following will change:

For this question part a the sides you have are the hypotenuse which is 225, and the adjacent which you are assuming to be 70. You need to use the Cos ratio to check if the angle works out to be 75 degrees. If it is then the ladder is safe at 70m distance. If not, then it's not.

For part b, you are looking for the height of the wall which is the opposite side. So use Sin ration with 75 degree angle you have on the ground.

If the angle 75 deg is in the air, then part a will be the Sin ratio and for part b you would use the Cos ratio.

Hope this helps, and good luck!

The angle y is on the ground. For the Cos Ratio adj/hyp I'm getting 70/225=0.31111 I have a feeling I'm not doing it right though

theLuggage

Ok lets do it step by step:

So Cos A = adj/hyp
Cos A = 70/225
A = Cos Inverse (70/225)
A = 71.87....degrees.

Therefore ladder is unsafe as 71 deg < 75 deg.

I don't think you were using Cos Inverse. (Looks like Cos to the power of minus 1)
Remember when Sin, Cos or Tan are separated from their angle, you must use inverse to work out the degrees.

theLuggage

Part b then.

The ladder is now safe so it must be 75 degree angle so:

Sin A = opp/hyp
Sin 75 = x/225 (calling the unknown opp side x)
225(Sin 75) = x
217.3333... = x
217cm = x

Atlas26

didn't see reply
nevermind

theLuggage

No what you had is perfect! Well done

Atlas26

theLuggage wrote: »

Ok lets do it step by step:

So Cos A = adj/hyp
Cos A = 70/225
A = Cos Inverse (70/225)
A = 71.87....degrees.

Therefore ladder is unsafe as 71 deg < 75 deg.

I don't think you were using Cos Inverse. (Looks like Cos to the power of minus 1)
Remember when Sin, Cos or Tan are separated from their angle, you must use inverse to work out the degrees.

Yeah, I wasn't doing the Cos Inverse. Thanks a million you've been very helpful!!

Atlas26

theLuggage wrote: »

No what you had is perfect! Well done

Yeah but the online calculator was not giving me the inverse

theLuggage

Atlas26 wrote: »

Yeah but the online calculator was not giving me the inverse

Likewise! Had to dig out my real calculator

Atlas26

Really need to do more Trig my teacher wasn't the best tbh. You were great!