Given A triangle with sides x=6.35 cm and Y=12.25 cm with an angle of 90 degrees between them, find the length of the hypotenuse and the size of the other two angles.

Hypotenuse = 13.798 cm, Angle1 = 27.4° and Angle2 = 62.59°

Step-by-step explanation:

The first step to help us understand the question would be to draw it out.

A right angled triangle, with the two sides that make the right angle being x and y (it does not matter which way you put x and y).

I have attached the quick sketch I will refer to.

To find the length of the hypotenuse (lets call it H) we can use Pythagoras theorem as shown below

Substitute in our values for x and y, and solve for H

H = 13.79 cm

To find the other two angles of the triangle we will use trigonometry

I will first look for angle ∅. Since we have all three sides of the triangle we can use any of the three trig functions, I chose to use Tan

Tan ∅

Substitute in our values for x and y, and solve for ∅

Tan ∅ =

∅ =

∅ = 27.4°

Now do the same for angle β. I chose to use Tan again

Tan β

Substitute in our values for x and y, and solve for β

Tan β =

β =

β = 62.59°

answer: 59

step-by-step explanation:

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.