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

angle a = arctan(5/7) = 35.5

angle b = arctan(7/5) = 54.5

Answer is C

Answer 2

Answer:

(C)35.5° and 54.5°

Step-by-step 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

$\frac{BC}{AC}=tanA$

$\frac{5}{7}=tanA$

$0.714=tanA$

$A=tan^{-1}(0.714)$

$A=35.5^{\circ}$

Again, from ΔABC, we have

$\frac{AC}{BC}=tanB$

$\frac{7}{5}=tanB$

$1.4=tanB$

$B=tan^{-1}(1.4)$

$B=54.5^{\circ}$

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

Thus, option C is correct.