Across the Lake

Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 1 of 37.

How far is the tree from post A? A and B are 150 m apart, with angles 48° and 64°.

$Posts A and B 150 m apart, the tree T across the lake, angles 48°, 64° and 68°$

Each side divided by the sine of the opposite angle gives the same number for every side.

$\frac{a}{\sin\left(A\right)} = \frac{b}{\sin\left(B\right)}$

The distance d from A to the tree is across from the 64° at B. So $\frac{d}{\sin\left(64^{\circ}\right)} = \frac{150}{\sin\left(68^{\circ}\right)}$ : d ≈ 145.41 m.

Challenge

Two posts A and B stand 120 m apart on the shore. The angle to the tree T is 52° at A and 61° at B. So the angle at the tree is 67°. Find the distance x from A to the tree. Done means x is in metres with 2 decimals.

Then press Check.

Try it yourself

$Use the figure to find x$