Question

Please help.

Trigonometry
Objective: Use trigonometry functions to find the area of triangles.
In an isosceles Δ, the two equal sides each measure 26 meters, and they include the angle of 31*. Find the area of the isosceles triangle to the nearest square meter.

Answer 1

174 m²

Explanation:

½ × 26 × 26 × sin(31)

174.0828693

Answer 2

173.97

Explanation:

so first we have to find the other side length by using the law of cosines. using this law we are able to find a length of a side with the opposite angle measurement and the 2 side lengths.

first we are going to set up out problem...

so lets say that the opposite side is going to be a the right side is going to be b and the left side is going to be c

a²=b²+c²-2·b·c·cosФ

so now we plug in the numbers

a²=26²+26²-2·26·26·cos(31)

simplify like this

a²=26²+26² =1352

- (don't forget the subtraction sign)

2·26·26·cos(31) = 1158.89

now we plug that back in to get...

a²=1352-1158.89

now we do a little math

a²= 193.11

then we square root to get the a by itself and we get (√a²= √193.11)

and we get a = 13.89

now we have all of the side length the have to find the height to finish our problem. we are going to cut this shape in half to make a right triangle

now out bottom length will be 6.94

now we use the pythagorean theorem

a²+6.94²=26²

now in this situation don't get confused a is going to be out height

now we solve

a²+48.16=676

-48.16 -48.16

a²=627.84

then the square root each side........

√a²=√627.84

and we get

a=25.05 this is our height

now to solve for the area

(b · h)/2

plug in

(13.89 · 25.05)/2

347.94/2

173.97 there is our answer