7)

Find the values of the sine, cosine, and tangent for ZA C A 36ft B 24ft

Reptile [31]

<h2>Question:</h2>

Find the values of the sine, cosine, and tangent for ∠A

a. sin A = $\frac{\sqrt{13} }{2}$ , cos A = $\frac{\sqrt{13} }{3}$ , tan A = $\frac{2 }{3}$

b. sin A = $3\frac{\sqrt{13} }{13}$ , cos A = $2\frac{\sqrt{13} }{13}$ , tan A = $\frac{3}{2}$

c. sin A = $\frac{\sqrt{13} }{3}$ , cos A = $\frac{\sqrt{13} }{2}$ , tan A = $\frac{3}{2}$

d. sin A = $2\frac{\sqrt{13} }{13}$ , cos A = $3\frac{\sqrt{13} }{13}$ , tan A = $\frac{2 }{3}$

<h2>Answer:</h2>

d. sin A = $2\frac{\sqrt{13} }{13}$ , cos A = $3\frac{\sqrt{13} }{13}$ , tan A = $\frac{2 }{3}$

<h2>Step-by-step explanation:</h2>

The triangle for the question has been attached to this response.

As shown in the triangle;

AC = 36ft

BC = 24ft

ACB = 90°

To calculate the values of the sine, cosine, and tangent of ∠A;

i. First calculate the value of the missing side AB.

Using Pythagoras' theorem;

⇒ (AB)² = (AC)² + (BC)²

Substitute the values of AC and BC

⇒ (AB)² = (36)² + (24)²

Solve for AB

⇒ (AB)² = 1296 + 576

⇒ (AB)² = 1872

⇒ AB = $\sqrt{1872}$

⇒ AB = $12\sqrt{13}$ ft

From the values of the sides, it can be noted that the side AB is the hypotenuse of the triangle since that is the longest side with a value of $12\sqrt{13}$ ft (43.27ft).

ii. Calculate the sine of ∠A (i.e sin A)

The sine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the hypotenuse side of the triangle. i.e

sin Ф = $\frac{opposite}{hypotenuse}$ -------------(i)

In this case,

Ф = A

opposite = 24ft (This is the opposite side to angle A)

hypotenuse = $12\sqrt{13}$ ft (This is the longest side of the triangle)

Substitute these values into equation (i) as follows;

sin A = $\frac{24}{12\sqrt{13} }$

sin A = $\frac{2}{\sqrt{13}}$

Rationalize the result by multiplying both the numerator and denominator by $\sqrt{13}$

sin A = $\frac{2}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }$

sin A = $\frac{2\sqrt{13} }{13}$

iii. Calculate the cosine of ∠A (i.e cos A)

The cosine of an angle (Ф) in a triangle is given by the ratio of the adjacent side to that angle to the hypotenuse side of the triangle. i.e

cos Ф = $\frac{adjacent}{hypotenuse}$ -------------(ii)

In this case,

Ф = A

adjacent = 36ft (This is the adjecent side to angle A)

hypotenuse = $12\sqrt{13}$ ft (This is the longest side of the triangle)

Substitute these values into equation (ii) as follows;

cos A = $\frac{36}{12\sqrt{13} }$

cos A = $\frac{3}{\sqrt{13}}$

Rationalize the result by multiplying both the numerator and denominator by $\sqrt{13}$

cos A = $\frac{3}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }$

cos A = $\frac{3\sqrt{13} }{13}$

iii. Calculate the tangent of ∠A (i.e tan A)

The cosine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the adjacent side of the triangle. i.e

tan Ф = $\frac{opposite}{adjacent}$ -------------(iii)

In this case,

Ф = A

opposite = 24 ft (This is the opposite side to angle A)

adjacent = 36 ft (This is the adjacent side to angle A)

Substitute these values into equation (iii) as follows;

tan A = $\frac{24}{36}$

tan A = $\frac{2}{3}$

6 0

3 years ago

Lesson 13 Problem Set 5.4

Elan Coil [88]

5.4 fhhdfbf help gta that’s tuff my boys

4 0

3 years ago

Six groups of students sell 162 balloons at a carnival.There are 3 students in a group.If each student sells the same number how

natima [27]

Answer:

9

Step-by-step explanation:

there are 6 groups of 3 students, that is

number of students = 6 × 3 = 18

They each sell the same number of balloons, thus

$\frac{162}{18}$ = 9 balloons each

8 0

4 years ago

When angles are complementary, the sum of their measures is 90 degrees.Two complementary angles have measures of 2x-10 degrees a

Mariana [72]

Complementary angles are those angles whose sum is 90 degree.

The measurement of two complementary angles are

$(2x-10), (3x-10)$

There sum have to be 90 degree. That is

$2x-10+3x-10 = 90$

Combining like terms ,

$5x - 20 = 90$

Moving 20 to right side

$5x=110$

Dividing both sides by 5

$x =22$

So the measurement of the angles are

$2*22-10 , 3*22-10 \\
34 degree, 56 degree$

6 0

4 years ago

Simplify the following expressions: 1/3(6a+12)+3a

Maru [420]

Answer in simplified expression: 5a+4

3 0

4 years ago

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