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Precalculus : Trigonometric Applications

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12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Area Of A Triangle

What is the area of a triangle with sides , , and ?

Possible Answers:

$area=100\sqrt{2}$

area=200

$area=10\sqrt{2}$

area=10

$area=20\sqrt{2}$

Correct answer:

$area=10\sqrt{2}$

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

$s=\frac{1}{2}(a+b+c)$

where , , are the sides of a triangle.

Then the area is

$area=\sqrt{s(s-a)(s-b)(s-c)}$

So if we plug in

$s=\frac{1}{2}(6+5+9)$

$s=\frac{1}{2}(20)$

s=10

So the area is

$area=\sqrt{10(10-6)(10-5)(10-9)}$

$area=\sqrt{200}$

$area=10\sqrt{2}$

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Example Question #1 : Area Of A Triangle

What is the area of a triangle with side lengths of , , and ?

Possible Answers:

area= 5

area= 7.5

area= 12

area=6

area= 7

Correct answer:

area=6

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

$s=\frac{1}{2}(a+b+c)$

where , , are the sides of a triangle.

Then the area is

$area=\sqrt{s(s-a)(s-b)(s-c)}$

So if we plug in

$s=\frac{1}{2}(3+4+5)$

$s=\frac{1}{2}(12)$

s=6

So the area is

$area=\sqrt{6(6-3)(6-4)(6-5)}$

$area=\sqrt{36}$

area=6

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Example Question #5 : Area Of A Triangle

What is the area of a triangle with side lengths , , and ?

Possible Answers:

area=32.5

area=900

area=33

area=30

area=20

Correct answer:

area=30

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

$s=\frac{1}{2}(a+b+c)$

where , , are the sides of a triangle.

Then the area is

$area=\sqrt{s(s-a)(s-b)(s-c)}$

So if we plug in

$s=\frac{1}{2}(5+12+13)$

$s=\frac{1}{2}(30)$

s=15

So the area is

$area=\sqrt{15(15-5)(15-12)(15-13)}$

$area=\sqrt{900}$

area=30

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Example Question #11 : Area Of A Triangle

What is the area of a triangle with side lengths , , and ?

Possible Answers:

area=7056

area=84

area=87.5

area=80

area=16

Correct answer:

area=84

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

$s=\frac{1}{2}(a+b+c)$

where , , are the sides of a triangle.

Then the area is

$area=\sqrt{s(s-a)(s-b)(s-c)}$

So if we plug in

$s=\frac{1}{2}(7+24+25)$

$s=\frac{1}{2}(56)$

s=28

So the area is

$area=\sqrt{28(28-7)(28-24)(28-25)}$

$area=\sqrt{7056}$

area=84

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Example Question #12 : Area Of A Triangle

What is the area of a triangle with side lengths , , and ?

Possible Answers:

area=21

$area=21\sqrt{2}$

$area=4\sqrt{21}$

$area=2\sqrt{21}$

Correct answer:

$area=2\sqrt{21}$

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

$s=\frac{1}{2}(a+b+c)$

where , , are the sides of a triangle.

Then the area is

$area=\sqrt{s(s-a)(s-b)(s-c)}$

So if we plug in

$s=\frac{1}{2}(5+5+4)$

$s=\frac{1}{2}(14)$

s=7

So the area is

$area=\sqrt{7(7-5)(7-5)(7-4)}$

$area=\sqrt{84}$

$area=2\sqrt{21}$

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Example Question #21 : Trigonometric Applications

What is the area of a triangle with side lengths , , and ?

Possible Answers:

area=8

$area=4\sqrt{2}$

area=2

area=4

$area=2\sqrt{2}$

Correct answer:

$area=2\sqrt{2}$

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

$s=\frac{1}{2}(a+b+c)$

where , , are the sides of a triangle.

Then the area is

$area=\sqrt{s(s-a)(s-b)(s-c)}$

So if we plug in

$s=\frac{1}{2}(3+3+2)$

$s=\frac{1}{2}(8)$

s=4

So the area is

$area=\sqrt{4(4-3)(4-3)(4-2)}$

$area=\sqrt{8}$

$area=2\sqrt{2}$

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Example Question #14 : Area Of A Triangle

What is the area of a triangle if the sides of a triangle are , , and ?

Possible Answers:

$area=\sqrt{5}$

$area=\sqrt{15}$

$area=4\sqrt{5}$

$area=16\sqrt{5}$

$area=4\sqrt{5}$

Correct answer:

$area=\sqrt{15}$

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

$s=\frac{1}{2}(a+b+c)$

where , , are the sides of a triangle.

Then the area is

$area=\sqrt{s(s-a)(s-b)(s-c)}$

So if we plug in

$s=\frac{1}{2}(4+2+4)$

$s=\frac{1}{2}(10)$

s=5

So the area is

$area=\sqrt{5(5-4)(5-2)(5-4)}$

$area=\sqrt{15}$

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Example Question #22 : Trigonometric Applications

The triangular fence of the T-rex in Jurassic park has sides a,b, and c measuring 100m, 110m, and 120m respectively. What is area of its enclosure?

Possible Answers:

A=2,152m^2

A=5,521m^2

A=5,152m^2

A=5,251m^2

A=2,512m^2

Correct answer:

A=5,152m^2

Explanation:

Use Heron's formula to calculate the area:

$A=\sqrt{s(s-a)(s-b)(s-c)}$

A, B, and C are side lengths and s is calculated by:

$s=\frac{a+b+c}{2}$ .

Calculate s:

$s=\frac{100+110+120}{2}=165$

Plug side lengths and s into Heron's formula:

$\\A=\sqrt{165(165-100)(165-110)(165-120)}\\ \\=\sqrt{165(65)(55)(45)}\\ \\=5,152m^2$

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Example Question #16 : Area Of A Triangle

Find the area of this triangle:

Tri area h

Possible Answers:

12.25 un^2

10.83 un^2

6.25 un^ 2

4.87 un^2

Correct answer:

10.83 un^2

Explanation:

Use Heron's Formula

$area = \sqrt{s (s - a)(s-b)(s-c)}$

where $s = \frac{ 1}{2} (a + b + c )$

and a=5, b=5, c=5

we can find to be:

$s = \frac{ 1}{2} ( 5 + 5 + 5 ) = 7.5$ .

From here, plug in all our known values and solve.

$\\area = \sqrt{ 7.5 ( 7.5 - 5 ) (7.5 - 5 ) ( 7.5 - 5 )} \\ \\= \sqrt{ 7.5 (2.5 )^3 } \approx 10.83$

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Example Question #17 : Area Of A Triangle

Find the area of this triangle:

Tri area g

Possible Answers:

14.83 un^ 2

16.19 un^ 2

4.69 un^ 2

20.98 un^ 2

Correct answer:

20.98 un^ 2

Explanation:

To find the area, use Heron's Formula,

$area = \sqrt{s(s-a) (s - b )(s - c )}$

where

$s = \frac{ 1}{ 2} (a + b + c )$

and

a=6, b=7, c=9 .

Here,

$s= \frac{ 1}{2} ( 6 + 7 + 9 ) = \frac{ 1}{2} \cdot 22 = 11$ .

Now plug in all known values and solve.

$\\ area = \sqrt{ 11 (11- 6 ) ( 11 - 7 ) ( 11 - 9 )} \\ \\= \sqrt{ 11 \cdot 5 \cdot 4 \cdot 2 } \approx 20.98$

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Precalculus : Trigonometric Applications

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Area Of A Triangle

Example Question #1 : Area Of A Triangle

Example Question #5 : Area Of A Triangle

Example Question #11 : Area Of A Triangle

Example Question #12 : Area Of A Triangle

Example Question #21 : Trigonometric Applications

Example Question #14 : Area Of A Triangle

Example Question #22 : Trigonometric Applications

Example Question #16 : Area Of A Triangle

Example Question #17 : Area Of A Triangle

All Precalculus Resources

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