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schepotkina [342]
3 years ago
15

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

enuse of the triangle?
Mathematics
2 answers:
Lana71 [14]3 years ago
8 0

The hypotenuse of the triangle is 29.23 cm long

<u>Solution:</u>

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

ankoles [38]3 years ago
4 0

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:

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