Question

In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 8 m?
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? m

Answer 1

The length of the hypotenuse would be 16. Since the hypotenuse is 2 times the length of the shorter leg, you simply multiply 8 by 2. (I apologise for my bad sketch of a triangle.)

Answer 2

The hypotenuse is 16m.

Triangle

A shape that has three sides and three angles are called a triangle.

Given

The Angles of the triangle are 30, 60, and 90 degrees.

And the shortest side is 8m.

Solution

In $\Delta ABC$,

$\angle A = 30\\ \angle B = 90\\ \angle C = 60$

Then BC becomes the shortest distance.

Then by trigonometry

$sin \alpha = \dfrac{Perpendicular}{ Hypotenuse}$

$\alpha = 30 \\ And\ Perpendicular = 8$

$sin30= \dfrac{8}{hypotenuse } \\\\ \dfrac{1}{2}= \dfrac{8}{hypotenuse } \\\\ Hypotenuse= 16m$

Thus, the hypotenuse is 16m.

More about the triangles link is given below.

https://brainly.com/question/25813512