MrCedi032106
Answered

Sketch and solve the following triangles.

1. The legs of a right triangle measure 5cm and 12cm. What is the measure of its hypotenuse?

2. In ∆ABC and C is a right angle, if c = 12 and b = 10, find cos A.

3. In ∆ABC and C is a right angle, the opposite of ∠A = 12. if the hypotenuse = 13, find tan θ.

4. If sin A = [tex] \frac{15}{17} [/tex] What is tan A?

5. If cot θ = [tex] \frac{7}{24} [/tex] What is sec θ?

[tex]\large\tt{(Nonsense \: will \: be)} \\ \large \tt{( \: reported!)} [/tex]




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Answer :

mhanifa

Answer:

#1

Use Pythagorean:

  • c² = a² + b²

Apply to given and find c:

  • c² = 5² + 12²
  • c² = 169
  • c = √169
  • c = 13 cm

#2

  • cos = adjacent / hypotenuse
  • cos A = b/c
  • cos A = 10/12 = 5/6

#3

  • Assumed θ is ∠A, this is not too clear

We have:

  • a = 12
  • c = 13

We know that:

  • tan A = a/b

Find b:

  • b = √c² - a² = √13²-12² = √25 = 5

So

  • tan A = 12/5

#4

Given

  • sin A = 15/17

We know that:

  • sin A = a/c, so a = 15 and c = 17
  • tan A = a/b

Find b:

  • b = √c² - a²= √17²-15²= √64 = 8

So

  • tan A = a/b = 15/8

#5

Given

  • cot θ = 7/24

We know:

  • cot = adjacent / opposite
  • sec = 1/cos = hypotenuse / adjacent

From the cot we have:

  • adjacent = 7, opposite = 24

Hypotenuse is:

  • √24² + 7² = √625 = 25

So,

  • sec θ = 25/7

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