University:
East Georgia State College
Course:
MATH 1540 | Calculus I
Academic year:

2024
Views:

493

Pages:

1
Author:

somospumasl3o

Question 1 In triangle ABC, angle B is five times as large as angle A. The measure of angle C is 2° less than that of angle A. Find the measures of the angles. (Hint: The sum of the angle measures is 180°.) Answer: We are given: 𝐴 = 𝑥 , 𝐵 = 5 𝑥 , 𝐶 = 𝑥 − 2 A=x,B=5x,C=x−2 As hinted, the sum of the angle measures is 180 ° 180°: 𝐴 + 𝐵 + 𝐶 = 180 A+B+C=180 𝑥 + 5 𝑥 + ( 𝑥 − 2 ) = 180 x+5x+(x−2)=180 7 𝑥 − 2 = 180 7x−2=180 7 𝑥 = 182 7x=182 𝑥 = 26 x=26 So, the angle measures are: 𝐴 = 𝑥 = 26 ° A=x=26° 𝐵 = 5 𝑥 = 130 ° B=5x=130° 𝐶 = 𝑥 − 2 = 24 ° C=x−2=24° Question 2 How are the interior and exterior angles of a triangle related? Answer: The Exterior Angle Theorem states that the sum of the measurements of the two distant interior angles determines the measure of an exterior angle in a triangle (the angles that do not form a linear pair with the exterior angle). Example: Consider △ 𝐴 𝐵 𝐶 △ABC below: The exterior angle measures 𝑚 ∠ 𝐴 𝐶 𝐷 = 110 ° m∠ACD=110°, and the two remote interior angles have a sum of: 𝑚 ∠ 𝐴 + 𝑚 ∠ 𝐵 = 60 ° + 50 ° = 110 ° . m∠A+m∠B=60°+50°=110°. Therefore 𝑚 ∠ 𝐴 𝐶 𝐷 = 𝑚 ∠ 𝐴 + 𝑚 ∠ 𝐵 m∠ACD=m∠A+m∠B. Question 3 Find the length of the third side of the right triangle, if one side = 4 3 4 3 and the hypotenuse = 8. Answer: Using Pythagoras theorem: 𝑏 2 = ℎ 2 − ( 4 3 ) 2 b 2 =h 2 −(4 3 ) 2 𝑏 2 = 8 2 − ( 4 3 ) 2 b 2 =8 2 −(4 3 ) 2 𝑏 2 = 64 − 48 = 16 b 2 =64−48=16 𝑏 = 16 = 4 b= 16 =4