Question

The hypotenuse of a right triangle is 3 times as long as the shorter leg. find the measure of the angle between the shorter leg and the hypotenuse

Answer 1

Let α be the angle between the shorter leg and the hypotenuse
shorter leg = x
hypotenuse = 3x

$cos \alpha = \cfrac{x}{3x} = \cfrac{1}{3} \ \ \to \alpha \approx70.5^o$

Answer 2

The measure of the angle between the shorter leg and the hypotenuse,    $\theta$ = 70.53 °

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.

Given that:

Let us consider the shorter leg be 'x'.

and, the Hypotenuse be '3x '.

Using trigonometric functions,

$cos \theta= \frac{Base}{Hypotenuse}$

cos $\theta$ = x /3x

cos $\theta$ = 1/3

 $\theta$ = $cos^{-1}$ (1/3)

  $\theta$ = 70.53 °

Hence,  the measure of the angle between the shorter leg and the hypotenuse  70.53 °

Learn more about Trigonometric function here:

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