The figures are similar. find the area. the area of △ △ a b c is 15 square cm. the height of △ △ a b c is 5 cm and the height of △ △ d e f is 13 cm. find the area of △ △ d e f . round to the nearest square cm if necessary.

The area of triangle DEF is

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

To find the scale factor, divide the height of triangle DEF by the height of triangle ABC

Let

z ------> the scale factor

step 2

Find the area of triangle DEF

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z -----> the scale factor

x ----> the area of triangle DEF

y -----> the area of triangle ABC

we have

substitute and solve for x

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).

about 168 miles

step-by-step explanation: