Question

In a right triangle, angle A measures 20°. The side opposite angle A is 10 centimeters long. Approximately how long is the hypotenuse of the triangle?

Answer 1

The hypotenuse of the triangle is 29.23 cm long

Solution:

Given that In a right triangle, angle A measures $20^{\circ}$

The side opposite angle A is 10 centimeters long

Let a right triangle ABC having right angled at B

According to question, angle A is $20^{\circ}$

We know by angle sum property of triangle, the sum of all the angles of the triangle is 180 degree

$\begin{array}{l}{A^{\circ}+B^{\circ}+C^{\circ}=180^{\circ}} \\\\ {20^{\circ}+90^{\circ}+C^{\circ}=180^{\circ}} \\\\ {C^{\circ}=180^{\circ}-110^{\circ}} \\\\ {C^{\circ}=70^{\circ}}\end{array}$

$\text { We know } \sin \theta=\frac{\text { Perpendicular }}{\text { Hypotenuse }}$

$\begin{array}{l}{\sin A^{\circ}=(B C) \div(A C)} \\\\ {\sin 20^{\circ}=(10) \div(A C)} \\\\ {0.342=10 \div A C} \\\\ {A C=10 \div(0.342)} \\\\ {A C=29.23 \mathrm{cm}}\end{array}$

So, the hypotenuse is 29.23 cm long

Answer 2

Answer:

sin(x) is equal to opposite over hypotenuse, so you can set it up as

sin(20) = 10/x

x = 10/sin(20)

x = 29.2 cm

Step-by-step explanation: