Question

What are the missing angle measures in triangle ABC?

a.1.4° and 88.6°
b.18.6° and 71.4°
c.35.5° and 54.5°
d.44.4° and 45.6°

Answer 1

(C)35.5° and 54.5°

Explanation:

It is given that ABC is a right angled triangle which is right angled at C and AC=7 inches and CB=5 inches.

Now, using the trigonometry, we have

From ΔABC, we have

`(BC)/(AC)=tanA`

`(5)/(7)=tanA`

`0.714=tanA`

`A=tan^(-1)(0.714)`

`A=35.5^(\circ)`

Again, from ΔABC, we have

`(AC)/(BC)=tanB`

`(7)/(5)=tanB`

`1.4=tanB`

`B=tan^(-1)(1.4)`

`B=54.5^(\circ)`

Therefore, the measure of missing angles in triangle ABC are 35.5° and 54.5°respectively.

Thus, option C is correct.

Answer 2

angle a = arctan(5/7) = 35.5

angle b = arctan(7/5) = 54.5

Answer is C