Finding the Angles of Triangle and Solving Algebraic Expressions (Math Problem Sample)

Student’s Name
Professor’s Name
Course Number
Date
Task 8
In the triangle, cm and cm. Given that the area of the triangle is
cm2, find the possible values of the angle.
Solution:
Using the Area
Substitute the given values and simplify.
3654 = 54sinB54 Divide both sides by 54.
Therefore, sin B = 23
Angle B = 41.80 or 138.20 Final Answer
Find the exact value of, giving your answer in the form
.
Solution:
Substitute the value of tan 300, sin 1350 and cos 2100
= 13 6 (12)+4 (-32) Simplify.
= 13 62+-432
= 13 62-23 Use distributive property.
= 66-233
= 66-2
= -2 + (66)(66) Rationalizing the denominator.
= -2 + 6636 Simplify
= -2 + 666
= -2+6 Final Answer
Show that for a small angle , measured in radians, .
Solution:
Using the small angle approximations and ,
Prove that.
Solution:
Left-hand side
, using identities and
, cancel out
Simplify (36 + 4 . 27 ÷ 4 – 18) ÷ 5.
Solution:
(36 + 4 . 27 ÷ 4 – 18) ÷ 5 = (36 + 108 ÷ 4 – 18) ÷ 5 Use the MDAS rule.
= (36 + 27 – 18) ÷ 5 Simplify.
= (63 – 18) ÷ 5
= (45) ÷ 5
= 9 Final Answer
Proper aerobic exercise involves exercising at a person’s correct training heart rate. To
find the correct training heart rate the following formulas are used.