Question

I need help ASAP thank you!!

Answer 1

Answer:

Step-by-step explanation:

Hello!

a)

You have three triangles and you have to find the ratio of the adjacent sides to the angle 23.1º

Remember, considering a specific angle ∠, "the adjacent sides" are those that make contact with the angle and the "opponent side" is the one that is in the opposite side of the angle and the hypotenuse is the longest side of the right triangle, always opposed to the right angle.

First triangle, the adjacent sides, are

JL= 20.17m (hypotenuse)

JK= 18.55m

Ratio: $\frac{JK}{JL}= \frac{18.55}{20.17}= 0.9196= 0.92$

Second triangle, adjacent sides:

PR= 141.19m (hypotenuse)

PQ= 129.85m

Ratio: $\frac{PQ}{PR} = \frac{129.85}{141.19}= 0.9196= 0.92$

Third triangle, adjacent sides:

XZ= 181.53m (hypotenuse)

XY= 166.95m

Ratio: $\frac{XY}{XZ} = \frac{166.95}{181.53} = 0.9196= 0.92$

b)

Using the calculator you have to calculate the trigonometric ratios of 23.1º:

sin(23.1º)= 0.392= 0.39

cos(23.1º)= 0.9198= 0.92

tan(23.1º)= 0.426= 0.43

c)

To calculate the trigonometrical ratios manually you have to do as follows:

Consider the angle A

$sinA= \frac{opposite}{hypotenuse}$

$cosA= \frac{adjacent}{hypotenuse}$

$tanA= \frac{opposite}{adjacent}$

In item a) you calculated the ratios of the adjacent sides of the angle by the hypotenuse, this is equal to the cosine of the given angle.

I hope this helps!