Chapter Closure
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Exercise 139 Page 334
a Use the sine ratio.
b Use the tangent ratio.
c Use the cosine ratio.
d Use the Pythagorean Theorem.
e Use the tangent ratio.
f Use the sine ratio.
g Use the cosine ratio.
a x≈ 5.176 m
b x≈ 18.66 in
c θ ≈ 24.62^(∘)
d x ≈ 13.416 ft
e x ≈ 32^(∘)
f θ ≈ 53.1^(∘)
g y ≈ 25.8^(∘)
a We have been given the angle and hypotenuse, and we want to determine the opposite leg labeled x. Given this information, we have to use the sine ratio to calculate x.
sin θ =Opposite/Hypotenuse
SubstituteValues
Substitute values
sin 15^(∘)=x/20
▼
Solve for x
MultEqn
LHS * 20=RHS* 20
20sin 15^(∘) =x
RearrangeEqn
Rearrange equation
x=20sin 15^(∘)
UseCalc
Use a calculator
x=5.17638...
RoundDec
Round to 3 decimal place(s)
x≈ 5.176
b We have been given the angle and opposite leg and want to determine the adjacent leg labeled x. Given this information, we have to use the tangent ratio to calculate x.
c We have been given the hypotenuse and adjacent leg to an unknown angle labeled θ. Given this information, we have to use the cosine ratio to calculate θ.
d Since we know both legs of the right triangle, we can use the Pythagorean Theorem to find the hypotenuse.
e We have been given the adjacent and opposite leg of the angle labeled x. Given this information, we have to use the tangent ratio to calculate x.
f We have been given the hypotenuse and opposite leg of the angle labeled θ. Given this information, we have to use the sine ratio to calculate x.
g We have been given the hypotenuse and adjacent leg of the angle labeled y. Given this information, we have to use the cosine ratio to calculate x.
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