Peter leaves work and drives 10miles due south he then heads east for 11 miles to reach his home how far is Peter home from where he works round answer to nearest tenths place

14.9 miles

Step-by-step explanation:

In the image below, the side of the triangle a, represents; "Peter leaves work and drives 10miles due south".

The side of the triangle b represents; "he then heads east for 11 miles to reach his home"

The distance between his work and home is represented by side c of the triangle.

This is a tight angle triangle, hence pythagoras theorem would be applied in solving it.

This theorem states that the square of the hypotenuse of a right angle triangle is equal to the sum of the squares of the other two sides;

This means we have;

c² = a² + b²

c² = 10² + 11²

c = √(100+121)

c = 14.87

Rounding off to the nearest tenths = 14.9

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.