Answer :
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:
The hypotenuse of the triangle is 29.23 cm long
Solution:
Given that In a right triangle, angle A measures [tex]20^{\circ}[/tex]
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 [tex]20^{\circ}[/tex]
We know by angle sum property of triangle, the sum of all the angles of the triangle is 180 degree
[tex]\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}[/tex]
[tex]\text { We know } \sin \theta=\frac{\text { Perpendicular }}{\text { Hypotenuse }}[/tex]
[tex]\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}[/tex]
So, the hypotenuse is 29.23 cm long