Question

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 =
`(15)/(17)` What is tan A?

5. If cot θ =
`(7)/(24)` What is sec θ?


`\large\tt{(Nonsense \: will \: be)} \\ \large \tt{( \: reported!)}`




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Answer 1

#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