# Math Help - Using Tangent: Word Problem

1. ## Using Tangent: Word Problem

Hey Everyone! Today I am faced with the problem that has the answer of 75.64degrees figuring how to solve this word problem:

A ladder which is leaning against a wall makes an angle of 70degrees with the ground and reaches 5 m up the wall. The foot of the ladder is then moved 50 cm closer to the wall. Find the new angle that the ladder makes with the ground.

Thank You For the Help!

2. Originally Posted by flutterby
Hey Everyone! Today I am faced with the problem that has the answer of 63.86degrees figuring how to solve this word problem:

A ladder which is leaning against a wall makes an angle of 70degrees with the ground and reaches 5 m up the wall. The foot of the ladder is then moved 50 cm closer to the wall. Find the new angle that the ladder makes with the ground.

Thank You For the Help!
first of all, your "answer" is incorrect ... moving the foot of the ladder closer to the wall will make the angle between the ladder and the ground increase to a value larger than the initial 70 degrees.

let $x$ = initial distance the foot of the ladder is from the wall (in meters)

let $L$ = length of the ladder

$\theta$ = new angle between the ladder and the ground

three trig ratio equations can be set up ...

$\tan(70) = \frac{5}{x}$

$\cos(70) = \frac{x}{L}$

$\cos(\theta) = \frac{x-0.5}{L}$

... solve for $\theta$

you should get $\theta = 75.64^{\circ}$

3. Originally Posted by flutterby
Sorry this is the correct problem and answer. Today I am faced with the problem that has the answer of 75.64degrees figuring how to solve this word problem:

A ladder which is leaning against a wall makes an angle of 70degrees with the ground and reaches 5 m up the wall. The foot of the ladder is then moved 50 cm closer to the wall. Find the new angle that the ladder makes with the ground.

Thank You For the Help!

Also can you please explain using tangent only, thanks!

4. Originally Posted by flutterby

Also can you please explain using tangent only, thanks!
why only tangent?

5. Originally Posted by skeeter
why only tangent?
oh cuz I need to know how to solve with tangent only until I move on to the next chapter. I need to be proficient in tangent first and know how it works fully!

6. I don't know if this will help or not