Question

Please Help Quick!!! Will Mark The BRAINIEST!!! A triangular patch of grass in a park is bordered by walking paths. The longest path bordering the patch of grass measures 90 feet. The smallest path bordering the patch of grass measures 53 feet. The smallest angle formed by the paths bordering the patch of grass measures 36°. What is the measure of the largest angle of the triangular patch of grass? Round your answer to the nearest tenth of a degree. Show your work.
I'm very desperate right now. First person to answer CORRECTLY will get 45 points for my gratitude.

Answer 1

Answer:

Measure of the longest angle will be 86.5°

Step-by-step explanation:

Let the patch of grass is in the shape of ΔABC. This triangle is to be bordered by the walking path.

The longest path bordering the patch of grass is AB = 90 feet

Angle formed opposite to AB (longest path) = ∠C

Smallest path (side BC) bordering the patch of grass measures 53 feet.

Smallest angle A formed by the smallest path is 36°.

Now we have to find the measure of the largest angle C.

Now we apply sine rule in ΔABC,

$\frac{sin36}{53}=\frac{sinC}{90}$

$\frac{0.5878}{53}=\frac{sinC}{90}$

By cross multiplication

sinC = $\frac{(0.58778)(90)}{53}$

       = 0.99811

C = $sin^{-1}(0.99811)$

   = 86.48°≈ 86.5°

Therefore, measure of the longest angle will be = 86.5°

Answer 2

You just have to set up proportions, so 53 is to 36 as 90 is to what?

This would come out to be about 61 degrees

Work:
53:36 as 90:x

Then u cross multiply

53x = 36(90)

Then solve for x

(Which is approximately 61 degrees)