Right Triangles please solve

[betternur]

Suppose a right triangle ABC with it's right angle at C has a 25 degree angle at A and the opposite side a has a length 7.
What does the angle at B have a measure of in degrees?
What is the length of the hypoenuse rounded to one decimal place?

 

[Denis]

The measures of the three angles in a triangle total 180 degrees.

If you aren't familiar with this fact, or don't understand how to use this to calculate the measure of the angle at B, then you're possibly not quite ready to deal with hypotenuses, side lengths and the likes.

If this is the case, then I suggest a talk with your math teacher.

 

[soroban]

Hello, betternur!

Did you make a sketch?

Suppose a right triangle ABC with: \(\displaystyle \angle C= 90^o,\;\angle A = 25^o,\:a = 7.\)

it's right angle at C has a 25 degree angle at A and the opposite side a has a length 7.
(a) What does the angle at B have a measure of in degrees?
(b) What is the length of the hypoenuse rounded to one decimal place?

                        B
                        *
                     *  *
              c   *     *
               *        * 7
            *           *
         * 25°          *
    A *  *  *  *  *  *  * C
               b

(a) The first part is easy.
Since the angles of any triangle add up to 180°,
. . .we have: \(\displaystyle \:B \:=\:180^o\,-\,25^o\,-\,90^o \:=\:\L\fbox{65^o}\)


(b) We have: \(\displaystyle \L\:\sin25^o \:=\:\frac{7}{c}\)

Hence: \(\displaystyle \L\:c\:=\:\frac{7}{\sin25^o} \:=\:16.56341108\)

Therefore: \(\displaystyle \L\:c \:\approx\:16.6\) units.