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Introduction to Trigonometry Practice 1: Right Triangles and Basic Ratios

Section A: Sides and Basic Ratios

Question 1mcq
In right triangle ABCABC, ∠B=90∘\angle B=90^\circ and the selected angle is ∠A\angle A. Which side is the hypotenuse?
A.ACAC
B.ABAB
C.BCBC
D.The side opposite ∠A\angle A
Question 2mcq
In right triangle PQRPQR, ∠Q=90∘\angle Q=90^\circ. With respect to ∠P\angle P, which side is opposite?
A.PQPQ
B.PRPR
C.QPQP
D.QRQR
Question 3mcq
Which definition of sin⁡A\sin A is correct in a right triangle?
A.oppositeadjacent\frac{\text{opposite}}{\text{adjacent}}
B.hypotenuseopposite\frac{\text{hypotenuse}}{\text{opposite}}
C.oppositehypotenuse\frac{\text{opposite}}{\text{hypotenuse}}
D.adjacenthypotenuse\frac{\text{adjacent}}{\text{hypotenuse}}
Question 4mcq
For an acute angle AA in a right triangle, which ratio equals tan⁡A\tan A?
A.hypotenuseadjacent\frac{\text{hypotenuse}}{\text{adjacent}}
B.oppositeadjacent\frac{\text{opposite}}{\text{adjacent}}
C.adjacentopposite\frac{\text{adjacent}}{\text{opposite}}
D.adjacenthypotenuse\frac{\text{adjacent}}{\text{hypotenuse}}
Question 5mcq
If sin⁡A=513\sin A=\frac{5}{13}, what is cosec⁡A\cosec A?
A.135\frac{13}{5}
B.513\frac{5}{13}
C.1213\frac{12}{13}
D.1312\frac{13}{12}

Section B: Evaluate and Diagnose

Question 6mcq
Two right triangles have the same acute angle AA but different sizes. Why is sin⁡A\sin A the same in both?
A.The hypotenuse is always 11.
B.The opposite side is always the same length.
C.Only isosceles right triangles have trigonometric ratios.
D.The triangles are similar, so corresponding side ratios are equal.
Question 7mcq
In a right triangle, for angle AA, opposite side =8=8, adjacent side =15=15, and hypotenuse =17=17. What is cos⁡A\cos A?
A.815\frac{8}{15}
B.1715\frac{17}{15}
C.1517\frac{15}{17}
D.817\frac{8}{17}
Question 8mcq
A student says that in a 77-2424-2525 right triangle, tan⁡A=2524\tan A=\frac{25}{24} when opposite to AA is 77. What is the correct tan⁡A\tan A?
A.2524\frac{25}{24}
B.724\frac{7}{24}
C.247\frac{24}{7}
D.257\frac{25}{7}
Question 9mcq
If sin⁡A=35\sin A=\frac{3}{5} and the hypotenuse is 2020 cm, what is the side opposite AA?
A.1212 cm
B.1515 cm
C.1616 cm
D.203\frac{20}{3} cm
Question 10mcq
A student labels the side touching angle AA and not the hypotenuse as the opposite side. What is the error?
A.The hypotenuse changes with the selected angle.
B.The opposite side must touch angle AA.
C.There is no adjacent side in a right triangle.
D.That side is adjacent to AA, not opposite to AA.