1. ## 4 problems

Write an expression for tan x degrees and an expression for tan(90-x)degrees, in terms of a, b, and c. How is the tangent of an angle related to the tangent of the angle's complement?

Write and expression for (sin X degrees)squared + (cos x degrees) squared in terms of a, b, and c. Then use the Pythagorean Theorem to simplify your expression

A) Use triangel ACD to write expressions for p squared + q squared in terms of b and for p in terms of b and angle A.

B) Find a squared in terms of c, p and q. Give your answer in expanded form.

C) Use results from parts a and b to find an expression for a squared in terms of b, c and angle A

D) Use the results from part c to find the angle A round your final answer to the nearest tenth. (with this problem is triangle ABC with side lengths AB = 27 AC=32 BC= 23)

other problem:
when the sun is shining at a 62 degree angle of depression, a flagpole forms a shadow of length x feet. Later the sun shines at an angle of 40 degrees, and the shadow is 25 feet longer than before

a) Draw a picture of the scenario

B) write two expressions for the height of the flagpole in terms of x

C) how tall is the flagpole to the nearest tenth of a foot

Thanks a please show all work.

2. Originally Posted by abc123
...

other problem:
when the sun is shining at a 62 degree angle of depression, a flagpole forms a shadow of length x feet. Later the sun shines at an angle of 40 degrees, and the shadow is 25 feet longer than before

a) Draw a picture of the scenario

B) write two expressions for the height of the flagpole in terms of x

C) how tall is the flagpole to the nearest tenth of a foot

Thanks a please show all work. How about showing what you have done so far?
to a) see attachment

to b) Use the tan-function:

$\displaystyle \tan(62^\circ)=\dfrac hx$ ..... $\displaystyle \tan(40^\circ)=\dfrac h{x+25}$

to c) Solve the first equation for x: $\displaystyle x=\dfrac h{\tan(62^\circ)}$
and plug in the term of x into the second equation:

$\displaystyle \tan(40^\circ)=\dfrac h{\dfrac h{\tan(62^\circ)}+25}$

Solve for h. (For your confirmation only $\displaystyle x \approx 37.88$)