Question

An isosceles triangle has an area of 143 and base 11. Find the base angle

Answer 1

78° (to nearest degree)

*see step-by-step if higher degree of accuracy is needed*

Explanation:

Area of a triangle = 1/2 x base x height

⇒ 143 = 1/2 x 11 x height

⇒ height = 26

Isosceles triangle comprises 2 right triangles, each with base 11/2 and height 26.

Therefore, to determine base angle use tan trig ratio:

`\tan(\theta)=\frac{\textsf{opposite side}}{\textsf{adjacent side}}`

`\implies tan(\theta)=(26)/((11)/(2))=(52)/(11)`

`\implies tan(\theta)=78.05582281...`