Is my answers correct?? trig?help? ratios?

Question

1.) The legs of a right triangle measure 5 inches and 7 units. If theta is the angle between the 5-inch leg and the hypotenuse, cos theta=

 

I got .58.

 

SOH CAH TOA

 Cosine=adj/hypotenuse 

 

hyp=?

leg1=5

leg2=7

Sqrt(5^2+7^2)=~8.6

 

cosine= 5/8.6=.58

 

 

 

2). The angle of elevation to the top of a 30-story skyscraper is measured to be 3 degrees from a point on the ground 2,000 feet from the building. What is the height of the skyscraper to the nearest hundredth foot? 

 

I got 104.82

 

tan3degrees=x/2000=104.82

 

 

3). Choose the best answer. A 50-foot tree casts a shadow 75 feet long. The sine of the angle of elevation of the top of the tree to the sun is approximately _____.

 

I got .55

I have trouble figuring out which angle is theta!!! 

when i draw my triangle...is it the bottom angle or the one on the top?? Im confused.

 

Answer 1

Cece,

 

Congratulations!  All you answers check out!

 

The angle of elevation is measured from the horizontal to the hypotenuse, i.e. the "bottom" angle.