Question

Find all the missing sides and angles (picture attached)

Answer 1

`\boxed{x=73.74}`

`\boxed{y=16.26}`

`\boxed{z=25}`

Explanation:

Hello there!

Algebra 1

The first thing we should find is the missing angle

Because this is a right triangle we can solve it using the Pythagorean Theorem

The Pythagorean theorem states that the sum of the two legs squared equal the hypotenuse squared

the formula...
`a^2+b^2=c^2` where a and b = legs and c = hypotenuse

we are given two legs so we plug in a and b and solve for c

`7^2+24^2=c^2\\7^2=49\\24^2=576\\576+49=625\\625=c^2\\√(c^2) =c\\√(625) =25\\c=25`

so we can conclude that the missing side length ( or z) equals 25

now to solve for the angles

Trigonometry

We can solve for y using sin

sin = opposite side divided by the hypotenuse

the opposite of y is 7 and the hypotenuse is 25

so we set up an equation
`sin(y)=(7)/(25)`

now we solve for y

`(7)/(28) =.28\\arcsin(y)=y\\arcsin(.28)=16.26020471`

then we round to the nearest hundredth

so we can conclude that angle labeled y = 16.26

basic geometry

Remember all of the angles in a triangle add up to equal 180 so we can find x by subtract the known angles from 180

180 - 90 - 16.26 = 73.74 so we can conclude that x = 73.74