Two Triangles

Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 6 of 37.

$From C a side of length 6 meets the base at two points B₁ and B₂$

A = 30°, AC = 10 and BC = 6. Turn the side of length 6 around C. It meets the bottom line in two places, B₁ and B₂. So two different triangles have the same three facts.

$\sin\left(B\right) = \frac{5}{6}$ gives B about 56.44°. Also, $180^{\circ}-56.44^{\circ}$ = 123.56° has the same sine. 30° + 123.56° is less than 180°, so both triangles exist. This is called the ambiguous case: one set of facts, two triangles. Always check the large angle too.

Challenge

In triangle ABC, A = 35°, a = BC = 9 cm and b = AC = 14 cm. The angle θ at B is more than 90°, as drawn. Find θ. Done means θ is in degrees with 2 decimals, written with its ° sign.

Then press Check.

Try it yourself

$Use the figure to find theta$