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Chapter 13: Q30. (page 534)

a. Show that tan鈭燗 = slope of AC.

b. Use trigonometry to find m鈭燗.

Short Answer

Expert verified
  1. We showed thattan鈭�A=slopeofAC炉 .
  2. the value of鈭�A=38.65鈭� .

Step by step solution

01

Step-1 – Given

Given figure is:

02

Step-2 – To determine

We have to show that tan鈭�A=slopeofAC炉.

03

Step-3 – Calculation 

Slope formula with two points(x1,y1)鈥夆赌塧苍诲鈥夆赌�(x2,y2) is:

m=y2鈭�y1x2鈭�x1

The given points areA(0,0) andC(5,4) .

m=4鈭�05鈭�0=45=0.8

Also,

tan鈭�A=perpendicularBase=45=0.8.

Therefore, we proved thattan鈭�A=slopeofAC炉 .

04

Step-1 – Given

Given figure is:

05

Step-2 – To determine

We have to findm鈭�A .

06

Step-3 – Calculation 

Since,

tan鈭�A=perpendicularBase=45=0.8tan鈭�A=0.8鈭�A=tan鈭�1(0.8)鈭�A=38.65鈭�

So, the value of鈭�A=38.65鈭� .

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Most popular questions from this chapter

Find the slope of the line through the points named. If the slope is not defined, write not defined.

(6, -6); (-6, -6)

In Exercises 20 and 21 show that points P, Q, and R are collinear by showing that PQ and OR have the same slope.

P(-1, 3) Q(2, 7) R(8, 15)

Write an equation of the circle that has the given center and radius.

C(鈭�2,5)鈥夆赌夆赌�;鈥夆赌夆赌�r=13

In Exercises 28 and 29,

(a) find the lengths of the sides of triangle RST,

(b) use the converse of the Pythagorean Theorem to show that triangle RST is a right triangle, and

(c) find the product of the slopes of RT and ST.

29. R(4, 3), S(-3, 6), T(2, 1)

In Exercises 16-19 a point P on a line and the slope of the line are given. Sketch the line and find the coordinates of two other points on the line.

17. P(-3, 0); slope =25.
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