University:
Morehouse College
Course:
HMTH 105 | College Algebra 1
Academic year:

2024
Views:

159

Pages:

2
Author:

Reynaldo Wong

Question 1 In triangle DEF, side E is 4 cm long and side F is 7 cm long. If the angle between sides E and F is 50 degrees, how long is side D? Answer 1 This is a SAS triangle (two sides and an included angle), so we can use the Law of Cosines to find the length of side D: 𝐷 2 = 𝐸 2 + 𝐹 2 − 2 𝐸 𝐹 cos ⁡ 𝜃 D 2 =E 2 +F 2 −2EFcosθ 𝐷 2 = 4 2 + 7 2 − 2 ( 4 ) ( 7 ) cos ⁡ 5 0 ∘ D 2 =4 2 +7 2 −2(4)(7)cos50 ∘ 𝐷 2 = 65 − 56 cos ⁡ 5 0 ∘ D 2 =65−56cos50 ∘ 𝐷 = 65 − 56 cos ⁡ 5 0 ∘ D= 65−56cos50 ∘ 𝐷 ≈ 5.4 cm D≈5.4cm Question 2 What is the TSA formula of a right angle triangle? Answer 1 General formula for triangle area: 𝐴 𝑡 = 1 2 base × height A t = 2 1 base×height Formula for area of a right triangle: 𝐴 𝑡 = 1 2 𝑎 𝑏 A t = 2 1 ab where 𝑎 a and 𝑏 b are containing sides of the right angle and 𝑐 c is a hypotenuse. Question 3 Rephrase the sentences using the if-then format. Having two 45° angles is a sufficient condition for this triangle to be a right triangle. Answer 1 It is given that having two 45° angles is a sufficient condition for this triangle to be a right triangle. Let’s assume that 𝑝 p is the triangle with 45-degree angles and 𝑞 q is the right triangle. So, the statement in if-then form is given by: A triangle is a right triangle if it contains two 45-degree angles. Answer: The statements in if-then form is: If a triangle has two 45-degree angles, then the triangle is a right triangle. Question 4 Determine whether the set have a subset relationship. Are the two sets disjoint or equivalent? Do the set intersect? 𝐿 = { equilateral triangles } , 𝐸 = { equiangular triangles } L={equilateral triangles},E={equiangular triangles} Answer 1 The equilateral triangle is a triangle with all equal sides, and an equiangular triangle is a triangle with all equal angles. All angles of equilateral triangles will be equal, and all sides of equiangular triangles will also be equal. So, an equilateral triangle is an equiangular triangle, and an equiangular triangle is an equilateral triangle. Thus, 𝐿 L and 𝐸 E are equivalent sets.