Question

in the right triangle AB, mc=90, a=4, and sinA=1/2. what is the length of the hypotenuse?

Answer 1

Given:

In a right angle triangle ABC, $m\angle C=90^\circ , a=4$ and $\sin A=\dfrac{1}{2}$.

To find:

The length of the hypotenuse.

Solution:

It is given that $m\angle C$, so opposite side of this angle is the hypotenuse, i.e., c.

In a right angle triangle,

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

In the given triangle,

$\sin A=\dfrac{a}{c}$

Substituting the given values, we get

$\dfrac{1}{2}=\dfrac{4}{c}$

By cross multiplication, we get

$1\times c=4\times 2$

$c=8$

Therefore, the length of the hypotenuse is 8 units.