Question Type 7: Working with sine, cosine and area of triangle rule all together Exercises

Triangle ABC has $AB = 7$, $AC = 9$, and $\angle A = 50^\circ$. Find the area of triangle ABC, correct to 2 decimal places.

In triangle $ABC$, $\angle A = 71^\circ$, $\angle B = 48^\circ$, and $a = BC = 11\text{ cm}$. Find the area of triangle $ABC$, correct to 2 decimal places.

Using $\cos C = \frac{11}{16}$, compute the measure of angle $C$ in degrees (to one decimal place).

Triangle $ABC$ has $AB = 13$, $AC = 18$, and the included angle $\angle A = 120^\circ$. Find the circumradius $R$ of triangle $ABC$, correct to 2 decimal places.

In triangle $ABC$, $AB = 11$, $AC = 8$, and the area is $30 \text{ square units}$. Find all possible values of $BC$, correct to $2$ decimal places.

In triangle $ABC$, $BC = 9$, $AC = 12$, and $\angle A = 35^\circ$. Find all possible areas of triangle $ABC$, correct to 2 decimal places.

Let $A$ be the angle opposite the side of length $4x$ and the other two sides are given as $2x$ and $3x$. Find $A$ in degrees (to one decimal place).

Triangle ABC has sides $AB = 13$, $AC = 10$, and $BC = 15$. Find the area of triangle ABC, correct to 2 decimal places.

For a triangle with sides $2x$, $3x$, and $4x$, let $C$ be the angle opposite the side of length $3x$. Find $\cos C$.

In triangle ABC, $BC = 11$, $AC = 7$, and $\angle A = 52^\circ$. Find the area of triangle ABC, correct to 2 decimal places.

Triangle ABC has sides $AB = 9$, $AC = 13$, and $BC = 14$. Find the length of the altitude from $A$ to $BC$, correct to 2 decimal places.

Two sides of a triangular field meet at point $A$ with lengths $AB = 70\text{ m}$ and $AC = 85\text{ m.}$ The area is $2700\text{ m}^2$, and the angle at $A$ is obtuse. Find $BC$ to 1 decimal place.