Complete the following.
#1 - 3: Find the missing variable(s). Round to the nearest tenth.
Help please all three?

Step-by-step explanation:

1) From the given right angle triangle,

22 represents the hypotenuse of the right angle triangle.

With m∠21 as the reference angle,

x represents the opposite side of the right angle triangle.

To determine x, we would apply

the Sine trigonometric ratio.

Sin θ = opposite side/hypotenuse. Therefore,

Sin 21 = x/22

x = 22 Sin 21 = 22 × 0.3584

x = 7.9

2) From the given right angle triangle,

RS represents the hypotenuse of the right angle triangle.

With m∠S as the reference angle,

x represents the adjacent side of the right angle triangle.

To determine x, we would apply

the Cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse. Therefore,

Cos 33 = x/15

x = 15 Cos 33 = 15 × 0.8387

x = 12.6

3) From the given right angle triangle,

AB represents the hypotenuse of the right angle triangle.

With m∠A as the reference angle,

x represents the adjacent side of the right angle triangle.

y represents the opposite side of the right angle triangle.

To determine x, we would apply

the Cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse. Therefore,

Cos 32 = x/10

x = 10 Cos 32 = 10 × 0.848

x = 8.5

To determine y, we would apply

the Sine trigonometric ratio.

Sin θ = opposite side/hypotenuse. Therefore,

Sin 32 = y/10

y = 10 Sin 32 = 10 × 0.5299

y = 0.53

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.