body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Dashboard

McGraw Hill Glencoe Algebra 2, 2012 View details

1. Trigonometric Functions in Right Triangles

Finish the assignment

Continue to next subchapter

Exercise 20 Page 795

Draw a right triangle where sin B= 49. Use the trigonometric ratio to label two side lengths and the Pythagorean Theorem to find the missing side.

cos B=sqrt(65)/9, tan B=4sqrt(65)/65, csc B=9/4, sec B=9sqrt(65)/65, cot B=sqrt(65)/4

Practice makes perfect

In a right triangle, ∠ A and ∠ B are acute angles while ∠ C is the right angle. Sine is defined as the ratio of the opposite side of an angle to the hypotenuse. We are given that sin B= 49. sin = opp/hyp ⇒ sin B = 4 9 Now, let's draw a right triangle satisfying these conditions.

Let's find the adjacent side by substituting b= 4 and c= 9 into the Pythagorean Theorem.

a^2+b^2=c^2

SubstituteII

b= 4, c= 9

a^2 + 4^2 = 9^2

▼

Solve for a

CalcPow

Calculate power

a^2 + 16 = 81

SubEqn

LHS-16=RHS-16

a^2 = 65

SqrtEqn

sqrt(LHS)=sqrt(RHS)

a = sqrt(65)

Note that when solving the equation we only kept the principal root. This is because a represents a side length, and therefore, must be positive.

Now that we know the length of all three sides of the triangle, we can find the values of the five remaining trigonometric functions. Remember to rationalize denominators if needed.

Function	Substitute	Simplify
cos B=adj/hyp	cos B=sqrt(65)/9	cos B=sqrt(65)/9
tan B=opp/adj	tan B=4/sqrt(65)	tan B=4sqrt(65)/65
csc B=hyp/opp	csc B=9/4	csc B=9/4
sec B=hyp/adj	sec B=9/sqrt(65)	sec B=9sqrt(65)/65
cot B=adj/opp	cot B=sqrt(65)/4	cot B=sqrt(65)/4

Showing Our Work

Rationalizing Denominators

Rationalizing a denominator means eliminating the radical expression from the denominator. Let's rationalize the denominator of the expression 4sqrt(65). To do so, we will expand the fraction by multiplying the numerator and denominator by sqrt(65).

4/sqrt(65)

ExpandFrac

a/b=a * sqrt(65)/b * sqrt(65)

4sqrt(65)/sqrt(65)* sqrt(65)

ProdToPowTwoFac

a* a=a^2

4sqrt(65)/(sqrt(65))^2

PowSqrt

( sqrt(a) )^2 = a

4sqrt(65)/65

Let's now follow the same procedure to rationalize the denominator of 9sqrt(65).

9/sqrt(65)