⦁ 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.

Question

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Answer :

eudora eudora · Answer 1 · 2019-06-18T06:01:22-04:00

Answer:

Measure of largest angle of the triangular patch is 86.5°

Step-by-step explanation:

As shown in the figure attached.

ABC is the triangular park which is boarded by walking paths.

Longest side (path) of the triangle BC = 90 feet

Smallest side (path) of the triangle AC = 53 feet

Measure of angle given opposite to the smallest side = 53°

We have to calculate the measure of the angle opposite to the longest side.

We apply sine rule in ΔABC

[tex]\frac{sinB}{AC}=\frac{sinA}{BC}[/tex]

Now we put the values

[tex]\frac{sin36}{53}=\frac{sinA}{90}[/tex]

[tex]\frac{0.588}{53}=\frac{sinA}{90}[/tex]

Now we cross multiply

90×0.588 = 53×sinA

sinA = [tex]\frac{52.90}{53}[/tex]

sinA = 0.998

A = [tex]sin^{-1}(0.998)[/tex]

= 86.4768° ≈ 86.5°

Therefore, ∠A = 86.5° is the answer.

∠A = 90°