Question

Consider the right triangle shown below.Suppose the hypotenuse of this right triangle is r=7 cm long.Suppose that sin(θ)=0.629.y is how many times as large as r? ____times as large   What is the value of y?y=Suppose that cos(θ)=0.778.x is how many times as large as r? ______times as large   What is the value of x?x=

Answer 1

Answer:

y is 0.629 times as large as r

x is 0.778 times as large as r

y = 4.403

x = 5.446

Explanations:

From the right-angled triangle shown:

The opposite is the side facing the angle θ

Opposite = y

The Hypotenuse is the longest side of the triangle

Hypotenuse = r

The Adjacent is the third side

Adjacent = x

Suppose sinθ = 0.629

r = 7

`\begin{gathered} \sin \theta\text{ = }\frac{Opposite}{\text{Hypotenuse}} \\ 0.629\text{ = }(y)/(r) \\ 0.629\text{ = }(y)/(7) \\ y\text{ = 7(0.629)} \\ y\text{ is 0.629 times as large as r} \\ y\text{ = }4.403 \end{gathered}`

Suppose that cos θ = 0.778

and r = 7

`\begin{gathered} \cos \theta\text{ = }\frac{Adjacent}{\text{Hypotenuse}} \\ 0.778\text{ = }(x)/(r) \\ 0.778\text{ = }(x)/(7) \\ x\text{ = 0.778(7)} \\ x\text{ is 0.778 times as large as r} \\ x\text{ = }5.446 \end{gathered}`