Question

The ratio of the angle measures of the triangle are 3:1:5.if the longest side of the triangle is 15ft .the shortest side of the triangle is?

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Answer 1

≈ 5.2 ft

Explanation:

sum the parts of the ratio, 3 + 1 + 5 = 9 parts

Divide the angle sum of a triangle by 9 to find the value of one part of the ratio.

180° ÷ 9 = 20° ← value of 1 part of the ratio, then

3 parts = 3 × 20° = 60°

5 parts = 5 × 20° = 100°

The angles of the triangle are 100°, 60° and 20°

The longest side is opposite the largest angle in the triangle

The shortest side is opposite the smallest angle in the triangle.

Thus

the longest side is opposite 100°

the shortest side is opposite 20°

let x represent the shortest side and using the Sine rule

`(x)/(sin20)` =
`(15)/(sin100)` ( cross- multiply )

x × sin100° = 15sin20° ( divide both sides by sin100° )

x =
`(15sin20)/(sin100)` ≈ 5.2 ( to the nearest tenth )

Thus the shortest side is ≈ 5.2 ft

Answer 2

3ft

Explanation:

get the ratio of longest side which is 5over9 is equal to 15 what about 1 over 9 then u equate n get 3