Question

Suppose that triangle ABC is a right triangle with a right angle at C and hypotenuse C. Also note that a is the length of the side opposite angle A and b is the length of the side opposite angle B Given that b 13 and C - 15, determine the values indicated below. Round to four decimal places when needed a- degrees. degrees.

Answer 1

Answer:

The value of a is 7.4833. The value of $A=29.9262^0$ and $B=60.0735^0$.

Step-by-step explanation:

Consider the provided information.

The required figure is shown below:

We need to find the value of a.

Calculate the value of a by using Pythagorean theorem.

$a^2+b^2=c^2$

$a^2+(13)^2=(15)^2$

$a^2=225-169$

$a^2=56$

$a=7.4833$

Hence, the value of a is 7.4833.

Now find the value of angle A as shown:

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

$\sin A=\frac{7.4833}{15}$

$A=sin^{-1}(0.4989)$

$A=29.9262^0$

Find the value of angle B as shown:

$\sin B=\frac{b}{c}$

$\sin B=\frac{13}{15}$

$B=sin^{-1}(0.8667)$

$B=60.0735^0$

Hence, the value of $A=29.9262^0$ and $B=60.0735^0$.