RS = 20ST = 48TR = 52The side lengths of right triangle RST are given. Triangle RST is similar to triangle UVW, where S corresponds to V and T corresponds to W. What is the value of tan W ?
Correct answer: B. 5/12
- A. 5/13
- B. 5/12
- C. 12/13
- D. 12/5
Explanation
Choice B is correct. Given that the triangles RST and UVW are similar, angle T corresponds to angle W. In triangle RST, angle S is the right angle, making TR the hypotenuse. The side RS is opposite to angle T, and ST is adjacent to angle T. The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. Therefore, tan T = RS/ST = 20/48 = 5/12. Since angle T is equal to angle W, it follows that tan W = tan T = 5/12.Choices A and C are incorrect because they represent the sine and cosine of angle W, respectively, which are not relevant for finding the tangent. Choice D is incorrect as it represents the reciprocal of the tangent, which is cotangent.
Last updated
About Quantitative Reasoning
Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
Practise Quantitative Reasoning
505 free Quantitative Reasoning MCQs from Analytical and Logical Reasoning, each with the correct answer and an explanation. Unlimited attempts, no account needed.
Exams that ask Analytical and Logical Reasoning questions like this
Analytical and Logical Reasoning is on 24 papers prepared for on TestUstad, and all of them draw the same bank, so this question is worth knowing for every one of them.
Related questions
State whether a ∈ C, if {a} ⊂ A: i: A ⊆ B ii: B ⊆ C
If 2m=4x and 2w = 8x, what is m in terms of w?
The sum of the Series will be i) Tn = 7n -5 ii) 𝑑 = −5 iii) 𝑎 = 2 iv) 𝑛 = 16 Which two statements are sufficient to solve the given question?
If Lines AB||CD, then e = ?
Find the number of degrees in angle B?I. AC < BCII. Angle BCD = 100°III. Angle A + Angle B + Angle C = 180°IV. AB = BCV. ABC is an isosceles triangle Which two statements are sufficient to answer the question?