Question

If a = 7 and b = 11, what is the measure of ∠B? (round to the nearest tenth of a degree) A) 32.5° B) 39.2° C) 50.5° D) 57.5°

Answer 1

D) 57.5°

Explanation:

As the question is not complete. So, let's suppose it is a right angle triangle then, we can apply Pythagoras theorem to calculate the hypotenuse or the third side.

Pythagoras Theorem =
`c^(2)` =
`a^(2) + b^(2)`

a = 7 and b = 11

`a^(2)` = 49

`b^(2)` = 121

Plugging in the values, we will get:

`c^(2)` = 49 + 121

`c^(2)` = 170

c =
`√(170)`

To calculate the unknown angle B, we can use law of sine.

Law of sine =
`(a)/(sinA)` =
`(b)/(sinB)` =
`(c)/(sinC)`

So,

`(c)/(sinC)` =
`(b)/(sinB)`

`(√(170) )/(sin90)` =
`(11)/(sinB)`

Sin90 = 1

sinB =
`(11)/(√(170) )`

B =
`sin^(-1)` (
`(11)/(√(170) )`)

B = 57.5°