Question

Elizabeth is mountain climbing with Frank and has just climbed a 16-meter vertical rock face. Frank is standing 30 meters away from the bottom of the cliff, looking up at Elizabeth. How far away are Elizabeth and Frank?

Pythagorean theorem: word problems ⬆️
Please respond.

Answer 1

34m

Explanation:

To find:-

• Distance between Frank and Elizabeth.

Answer:-

We are here given that Elizabeth climbed up the mountain vertically 30m , and the distance between frank and the bottom of the mountain is 30m .

We are interested in finding out the distance between frank and Elizabeth. For that we will have to use Pythagoras theorem , in which;

`\rm\implies a^2+b^2 = h^2 \\`

Where h is the longest side of the triangle and a and b are two other sides. here we need to find out the longest side ( see attachment) .

So on substituting the respective values, we have;

`\rm\implies h^2 = (16m)^2+(30m)^2 \\`

`\rm\implies h^2 = 256m^2 + 900m^2 \\`

`\rm\implies h^2 = 1156m^2\\`

`\rm\implies h =√(1156 \ m^2) \\`

`\rm\implies \red{h = 34 m} \\`

Hence the distance between Elizabeth and Frank is 34m .