Question

1. complete the following blanks. (5 marks)

we can solve for all unknown sides and angles of any triangle as long as we are given at least
pieces of information and one of those pieces is a
. in order to solve for sides and/or
angles of right triangles we use these methods:
or
. in order to solve non - right triangles we use

Explanation:

• For any triangle (right - or non - right), by the laws of triangle congruence and the use of trigonometric laws (such as the Law of Sines and Law of Cosines), we need at least three pieces of information with one side.
• For right - triangles, the Pythagorean theorem (\(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a,b\) are the legs) and trigonometric ratios (\(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}},\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}},\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\)) are fundamental.
• For non - right triangles, the Law of Sines (\(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\)) and the Law of Cosines (\(c^{2}=a^{2}+b^{2}-2ab\cos C\), \(a^{2}=b^{2}+c^{2}-2bc\cos A\), \(b^{2}=a^{2}+c^{2}-2ac\cos B\)) are used.

Answer:

three; side; Pythagorean theorem; trigonometric ratios; Law of Sines; Law of Cosines