Question

The measure of angle BAC can be calculated using the equation sine super negative 1 (StartFraction 3.1 Over 4.5 EndFraction) equals x. Triangle A B C is shown. Angle A C B is a right angle. The length of hypotenuse A B is 4.5 inches and the length of C B is 3.1 inches. Angle C A B is x. What is the measure of angle BAC? Round to the nearest whole degree.

Answer 1

The hard part of this question is decoding the equation.

$\angle BAC = \arcsin\left( \dfrac{3.1}{4.5} \right)$

There's nothing to do but ask the calculator.

$\angle BAC = \arcsin\left( \dfrac{3.1}{4.5} \right) \approx 43.54^\circ$

Answer: 44°

Answer 2

The required measure of angle BAC is nearest to 44°.

Given that,

The measure of angle BAC can be calculated,

Using the equation sine super negative 1 (Start Fraction 3.1 Over 4.5 End Fraction) equals x.

The length of hypotenuse AB is 4.5 inches

And the length of CB is 3.1 inches. Angle CAB is x.

We have to determine,

What is the measure of BAC.

According to the question,

Triangle ABC is shown. Angle ACB is a right angle.

Then, sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse).

Therefore,

$sinx = \frac{Perpendicular}{hyptotenuse}$

Perpendicular = Adjacent length

$sinx = \frac{3.1}{4.5}$

$x = sin^{-1}(\frac{3.1}{4.5})\\\\x = 43.54degree\\\\x = 44 degree (approx)$

Hence, The required measure of angle BAC is nearest to 44°.

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