Write an expression for \cos \theta using the cosine rule for the following triangle:
Consider the triangle given below:
Consider the triangle given below:
Given \triangle ABC consists of angles A, B and C which appear opposite sides a, b and c respectively:
Consider the following triangle:
Find an expression for a^{2} by using Pythagoras' theorem in \triangle BCD.
Find an expression for h^{2} by using Pythagoras' theorem in \triangle ACD.
Find an expression for x in terms of \cos A.
Substitute your expressions for h^{2} and x into your expression for a^{2} to prove the cosine rule.
To use the cosine rule to find the length ofAC, which angle would need to be given?
Find the length of the missing side in each of the following triangles using the cosine rule. Round your answers to two decimal places.
In \triangle ABC, \cos C = \dfrac{8}{9}:
Find the exact length of side AB in centimetres.
In \triangle QUV, q = 5, u = 6 and \cos V = \dfrac{3}{5}. Find the value of v.
In \triangle QUV, v = 6, q = 10 and u = 12. Find the value of \cos U.
For each of the following triangles, find the value of the pronumeral in degrees. Round your answers to two decimal places.
For each of the following triangles, find \theta to the nearest degree:
Find the value of \theta in the following triangle. Round your answer to the nearest hundredth of a degree.
Find the value of B in the following triangle. Round your answer to the nearest second.
A teacher is writing exam questions for her maths class. She draws a triangle, labels the vertices A, B and C and labels the opposite sides a = 5, b = 8 and c = 15 respectively.
She wants to ask students to find the size of \angle A. Explain why there is an error with her question.
A triangle has sides of length 13 \text{ cm}, 15 \text{ cm} and 5 \text{ cm}. Find the value of x, the largest angle in the triangle to the nearest degree.
The sides of a triangle are in the ratio 4:5:8. Find \theta, the smallest angle in the triangle to the nearest degree.