Question

Find the altitude of an isosceles triangle with base 4.24 feet. The vertex angle of the triangle measures 85°

Trigonometric equation and identitie
ANSWERED
asked 2021-05-09
Find the altitude of an isosceles triangle with base 4.24 feet. The vertex angle of the triangle measures 85°

Answers (1)

2021-05-10

Let xx be the altitude of the isosceles triangle. Consider half of the triangle which is a right triangle having an angle of \(85^{\circ}/2=42.5^{\circ}\) whose adjacent side is the altitude xx and the side opposite is half the base \(4.242=2.12\) feet.

Using tangent ratio, we can write: \(\tan42.5^{\circ}=opp/adj=2.12/x\)

\(x=2.12/\tan42.5^{\circ}\)

Use a calculator in DEGREE mode: \(x \sim 2.32\) feet

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