Question

Can someone help me with this problem? It’s Special Right Triangles: Decimal Answer. Round to the nearest tenth. Thank you ! 10 points

Answer 1

Answer:

h = 1.4

c = 2.8

Step-by-step explanation:

For each problem, remember the special triangle side ratios then use a proportion. To solve, isolate the variable.

For the triangle with the variable h:

Since two of the angles are 45, this is an isosceles triangle. All isosceles triangles have two equal sides that are not the hypotenuse.

In a right isosceles triangle, the ratio for regular side to hypotenuse is 1 to √2.

$\frac{1}{\sqrt2} =\frac{h}{2} \\h = 2\frac{1}{\sqrt2} \\h = \frac{2}{\sqrt2} \\h = \frac{2\sqrt2}{2} \\h = \sqrt{2}$

h = √2

h ≈ 1.4

For the triangle with the variable c:

The is an equilateral triangle cut in half because the angles are 30 and 60.

The side ratio of altitude to hypotenuse is √3 to 2.

$\frac{\sqrt{3} }{2} =\frac{c}{4} \\\sqrt{3} = \frac{c}{2}\\2\sqrt3 = c$

c = 2√2

c ≈ 2.8