Atriangle has angles that measure 30°, 60°, and 90°. the hypotenuse of the triangle measures 10 inches
which is the best estimate for the perimeter of the triangle? round to the nearest tenth
20.0 in
23.1 in.
23.7 in.
27.4 in

23.7 inches.

Step-by-step explanation:

See the attached diagram.

A triangle ABC has angles that measure 30°, 60°, and 90°.

Now, the hypotenuse BC = 10 inches.

Then using trigonometry  

⇒ inches.

Again,

⇒ inches.

Therefore, the perimeter of the triangle ABC will be equal to (AB + BC + CA) = (5 + 10 + 8.66) = 23.66 inches ≈ 23.7 inches. (Answer)

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.