Question

Use the figure below to determine the length of sides b and c.

Answer 1

`b=5√(3)\ units,c=10\ units`

Explanation:

step 1

Find the value of c

we know that

In the right triangle of the figure

The sine of angle of 30 degrees is equal to divide the opposite side to the angle of 30 degrees by the hypotenuse

so

`sin(30^o)=(5)/(c)`

solve for c

`c=(5)/(sin(30^o))`

Remember that

`sin(30^o)=(1)/(2)`

substitute

`c=(5)/(0.5))`

`c=10\ units`

step 2

Find the value of b

Applying the Pythagorean Theorem

`c^2=b^2+5^2`

substitute the given values

`10^2=b^2+5^2`

`b^2=10^2-5^2`

`b^2=100-25`

`b^2=75`

`b=√(75)\ units`

simplify

`b=5√(3)\ units`

therefore

`b=5√(3)\ units,c=10\ units`