To find the value of a missing side in a right-angled triangle using trigonometry, we need to know the value of at least one angle (other than the right angle) and at least one side length.
For any pair of sides and a given angle, we can use one of these ratios to write the relationship between those three values.
Although we can write our values in some relationship using a trigonometric ratio, we still need to be able to turn our trigonometric function into a number.
We can evaluate trigonometric function expressions like \sin 42\degree and \cos 71\degree using the trigonometric functions on our calculator and entering the desired angle.
Once we have input a trigonometric function with some angle it is now a single term that we can multiply or divide by. To make sure that we are treating the trigonometric function as a single term, we need to keep an eye on our brackets.
When multiplying, \sin 42\degree \times 9 \neq \sin \left(42\degree \times 9\right) since the former multiplies the actual value while the latter multiples only the angle.
Similarly when dividing, \dfrac{\cos 71\degree}{9}\neq \cos \dfrac{71}{9}\degree since the former divides the actual value while the latter divides only the angle.
To avoid confusions, we try to always multiply on the left of a trigonometric function as a coefficient and express division using fractions. This gives us clearer expressions of the form 9\sin 42\degree and \dfrac{\cos 71\degree }{9}.
When evaluating trigonometric function expressions, make sure that your calculator is in degrees mode.
There is another way to refer to angle size called radians, but we are not using that for our calculations.
Evaluate 7\cos 77\degree to two decimal places.
We can evaluate trigonometric function expressions like \sin 42\degree and \cos 71\degree using the trigonometric functions on our calculator and entering the desired angle.
When evaluating trigonometric function expressions, make sure that your calculator is in degrees mode.
Based on where the angle is in the triangle and which pair of sides we are working with, we can choose one of the trigonometric ratios to describe the relationship between those values.
We can then rearrange that ratio to make our unknown value the subject of an equation and then evaluate to find its value.
Find the value of f correct to two decimal places.
Find the value of h correct to two decimal places.
A lighthouse is positioned at point A, and a boat is at point B. If d is the distance between the lighthouse and the boat, find d to two decimal places.
We can use the trigonometric ratios to find an unknown side length of a right angled triangle.
Once we set up our equation with a pronumeral representing the unknown side length, we can use inverse operations to make the pronumeral the subject of the equation.
Then we can evaluate the expression in our calculators to find the side length.