Right △EFG has its right angle at F, EG=8 , and FG=2 .
1 answer:
Answer:
Tan E = 2 / 7.75
Sin G = 7.75 / 8
Sec G = 4
Step-by-step explanation:
Find the attached document for better illustration of the triangle
Assuming the hypothenus of the triangle is 8 = EG since it's the longest side of the triangle.
FG = 2 = opposite side of the triangle.
We can use pythagorean theorem to find the adjacent of the triangle since we already know two sides.
EG² = FG² + EF²
EF² = EG² - FG²
EF² = 8² - 2²
EF² = 64 - 4
EF² = 60
EF = √(60)
EF = 7.7459 = 7.75
To find the respective trignometric ratio, we can use the relation SOH CAH TOA
Sine = opposite / hypothenus
Cosine = adjacent/ hypothenus
Tangent = opposite/ adjacent
A. tan E
Tan E = opposite/ adjacent
Tan E = 2 / 7.75
Tan E = 0.2580
B. Sin G = opposite / hypothenus
Sin G = 7.75 / 8
Sin G = 0.9687
C. Sec G = 1 / cos G
Cos G = adjacent / hypothenus
Sec G = 1 / (adjacent / hypothenus)
Sec G = hypothenus/ adjacent
Sec G = 8 / 2
Sec G = 4
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Answer:
c = 13.1
Step-by-step explanation:
* Lets explain how to solve the problem
- In Δ ABC
# ∠A is opposite to side a
# ∠B is opposite to side b
# ∠C is opposite to side c
- The sine rule is:
#
* Lets solve the problem
- In Δ ABC
∵ m∠A = 57°
∵ m∠B = 37°
∵ The sum of the measures of the interior angles of a triangle is 180°
∴ m∠A + m∠B + m∠C = 180°
∴ 57° + 37° + m∠C = 180°
∴ 94° + m∠C = 180° ⇒ subtract 94° from both sides
∴ m∠C = 86°
- Lets use the sine rule to find c
∵ a = 11 and m∠A = 57°
∵ m∠C = 86°
∵
- By using cross multiplication
∴ c sin(57) = 11 sin(86) ⇒ divide both sides by sin(57)
∴
* c = 13.1