Question

To find the distance across a river, a forester sets up stakes at A, B,C and D so that
stakes D and B are in line with a larger tree T, on the opposite bank. Calculate the
width of the river using the measurements given. (Upload a Picture of your solution)

Answer 1

Answer:

75m

Step-by-step explanation:

They are similar triangles: they have two corresponding angles: in a triangle with an angle of 90°, the other two will be of 45°.

Now that we know they are similar, we can calculate the ratio of the sides, by doing 10/2=5

We want to know the side AT, so we can do that by multiplying DC for 5:

DC = 15 × 5 = 75m

You can also check this by applying Pythagoras' Theorem:

DB =

$\sqrt{15^{2} + 2^{2} }$

Which equals 15.1 m

The hypotenuse of the other triangle is 15.1 × 5 = 75.5 m

Finally, we can apply for the last time the Pythagoras' Theorem to find AT:

$\sqrt{75.5^{2} - 10 {}^{2} }$

Which equals 74.8 = 75 m