Question

What is the approximate degree measure of angle A in the triangle below?

Answer 1

Answer-

$\boxed{\boxed{m\angle A=38^{\circ}}}$

Solution-

Given is that,

the triangle is a right angle triangle, where,

AC = Base = 18 units

BC = Perpendicular = 14 units

From the properties of trigonometry, we know that

$\tan \theta=\dfrac{\text{Perpendicular}}{\text{Base}}$

Putting the values,

$\Rightarrow \tan A=\dfrac{\text{BC}}{\text{AC}}$

$\Rightarrow A=\tan^{-1}\dfrac{\text{BC}}{\text{AC}}$

$=\tan^{-1}\dfrac{\text{14}}{\text{18}}$

$=\tan^{-1}0.78$

$=37.95\approx 38^{\circ}$

Therefore, the measurement of angle A is 38°

Answer 2

The degree measure of angle A in the triangle ACB is $\boxed{{{37.9}^ \circ }}$. Option (a) is correct.

Further explanation:

The Pythagorean formula can be expressed as,

$\boxed{{H^2} = {P^2} + {B^2}}.$

Here, H represents the hypotenuse, P represents the perpendicular and B represents the base.

The formula for tan of angle a can be expressed as

$\boxed{\tan a = \frac{P}{B}}$

Given:

The options are as follows,

(a). 37.9

(b). 38.9

(c). 51.1

(d). 52.1

Explanation:

The base of triangle ACB is AC.

The perpendicular of triangle ACB is BC.

The value of $\tan {{\theta }}$ can be expressed as,

$\tan {{\theta }} = \dfrac{{{\text{perpendicular}}}}{{{\text{base}}}}$

In triangle ACB the value of \tan A can be obtained as follows,

$\begin{aligned}\tanA &= \frac{{BC}}{{AC}}\\ \tan A &= \frac{{14}}{{18}}\\A &= {\tan ^{ - 1}}\left( {\frac{{14}}{{18}}} \right)\\A &= {\tan ^{ - 1}}\left( {0.778} \right)\\A &= {37.9^ \circ }\\\end{aligned}$

The degree measure of angle A in the triangle ACB is $\boxed{{{37.9}^ \circ }}$. Option (a) is correct.

Option (a) is correct.

Option (b) is not correct.

Option (c) is not correct.

Option (d) is not correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Trigonometry

Keywords: perpendicular, degree, angles A, sides, right angle triangle, triangle, altitudes, hypotenuse, on the triangle, hypotenuse, trigonometric functions.