MathematicsGrade 10en

📐 Right Triangle Trigonometry: Sine, Cosine, and Tangent

Master the fundamental trigonometric ratios and their applications in solving right triangles. **What you'll learn:** - Identify opposite, adjacent, and hypotenuse sides relative to a given angle - Calculate sine, cosine, and tangent ratios for acute angles - Solve for unknown side lengths using trigonometric ratios - Apply inverse trigonometric functions to find unknown angles - Use trigonometry to model and solve real-world problems

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Question 1
In a right triangle, the sine of an acute angle is equal to the ratio of the opposite side to the hypotenuse.
Question 2
In a right triangle, one acute angle measures $35°$ . Which trigonometric ratio would you use to find the length of the opposite side if you know the hypotenuse?
Question 3
In a right triangle with an acute angle of $50°$ , if the adjacent side is $8$ cm, the hypotenuse is ___ cm (rounded to the nearest tenth).
Question 4
The tangent of an angle in a right triangle depends on the length of the hypotenuse.
Question 5
A ladder leans against a vertical wall, forming a $65°$ angle with the ground. If the ladder is $10$ meters long, approximately how far up the wall does it reach?
Question 6
If $\cos(\theta) = 0.6$ , then $\theta = ___ °$ (rounded to the nearest whole number).
Question 7
In a right triangle, if $\tan(\theta) = \frac{7}{24}$ , what is $\sin(\theta)$ ?
Question 8
For complementary angles in a right triangle, the sine of one angle equals the cosine of the other angle.
Question 9
A surveyor measures an angle of elevation to the top of a building as $42°$ from a point $50$ meters away. The height of the building is ___ meters (rounded to the nearest tenth).
Question 10
Two right triangles are similar. In the first triangle, $\sin(A) = 0.8$ . What is $\sin(A)$ in the second triangle?