Chapter 13: Q30. (page 534)

a. Show that tan∠A = slope of AC.
b. Use trigonometry to find m∠A.

Short Answer

Expert verified

We showed that $\tan ∠ A = slopeof \bar{A C}$ .
the value of $∠ A = {38.65}^{\circ}$ .

Step by step solution

Step-1 – Given

Given figure is:

Step-2 – To determine

We have to show that $\tan ∠ A = slopeof \bar{A C}$ .

Step-3 – Calculation

Slope formula with two points $(x_{1}, y_{1}) and (x_{2}, y_{2})$ is:

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

The given points are $A (0, 0)$ and $C (5, 4)$ .

$m = \frac{4 - 0}{5 - 0} = \frac{4}{5} = 0.8$

Also,

$\tan ∠ A = \frac{perpendicular}{Base} = \frac{4}{5} = 0.8$ .

Therefore, we proved that $\tan ∠ A = slopeof \bar{A C}$ .

Step-1 – Given

Given figure is:

Step-2 – To determine

We have to find $m ∠ A$ .

Step-3 – Calculation

Since,

$\begin{array}{l} \tan ∠ A = \frac{perpendicular}{Base} = \frac{4}{5} = 0.8 \\ \tan ∠ A = 0.8 \\ ∠ A = \tan^{- 1} (0.8) \\ ∠ A = {38.65}^{\circ} \end{array}$

So, the value of $∠ A = {38.65}^{\circ}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

a. Show that tan∠A = slope of AC.
b. Use trigonometry to find m∠A.

Short Answer

Step by step solution

Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Statistics

Logic and Functions

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

a. Show that tan∠A = slope of AC.b. Use trigonometry to find m∠A.

Short Answer

Step by step solution

Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Statistics

Logic and Functions

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

a. Show that tan∠A = slope of AC.
b. Use trigonometry to find m∠A.