Question

Given the triangle below, find the angle θ in radians. Round to four decimal places.

Answer 1

Answer:

θ = 0.9626

Step-by-step explanation:

Hi there!

We're given the hypotenuse and the leg adjacent to θ in this right triangle. To find θ, we can use the cosine ratio:

$\displaystyle cos\theta=\frac{adjacent}{hypotenuse}$

Plug in the given information

$\displaystyle cos\theta=\frac{4}{7}$

Use the inverse cosine ratio

$\displaystyle \theta=cos^-^1(\frac{4}{7})$

Plug this into your calculator (and ensure you're solving for radians instead of degrees in the settings)

$\displaystyle \theta=0.9626$

Therefore, θ = 0.9626 when rounded to four decimal places.

I hope this helps!

Answer 2

Answer:

theta = 0.9626 radians

Step-by-step explanation:

cos theta = a/h

cos theta = 4/7 = 0.5714

so, the angle theta = arc cos 0.5714 =

55.1520 °

in radians => 55.1520 × π / 180°

= 0.9626 radians