Question

In right triangle ABC A=28° b=7 and

Answer 1

The correct answer option is C. B = 62°, a = 3.7, c = 7.9.

Explanation:

We have a right angled triangle, ABC, where A = 28° and b = 7.

We are to find the measure of angle B, and the lengths of side a and side c.

Angle B:

∠B = 180 - (90 + 28) = 62°

Side a:

`tan62=(7)/(a)`

a = 3.7

Side c:

`sin62=(7)/(c)`

c = 7.9

Answer 2

B = 62° , a = 3.7°, c = 7.9 ⇒ the 3rd answer

Explanation:

* In ΔABC

- a, b, c are the lengths of its 3 sides, where

# a is opposite to angle A

# b is opposite to angle B

# c is opposite to angle C

- m∠A = 28°

- m∠C = 90°

- b = 7

- At first lets find measure of angle B

∵ The sum of the measures of the interior angles in a triangle is 180°

∵ m∠B = 180 - (90 + 28) = 180 - 118 = 62°

* m∠B = 62°

* To solve the right triangle we can use the trigonometry functions

- sin∠B = b/c

∵ sin62° = 7/c ⇒ by using cross multiplication

∴ c = 7/sin62 = 7.9

- tan∠A = a/b

∵ tan28° = a/7 ⇒ by using cross multiplication

∴ a = 7 × tan28 = 3.7

∴ The length of the two sides a = 3.7 and c = 7.9 , m∠B = 62°

* B = 62° , a = 3.7°, c = 7.9