We have been given a right angled triangle, hypotenuse is known, and angle has been given. we need to find the adjacent side to the angle.

we use trigonometry ratios.
the ratio where we relate the hypotenuse and adjacent side is the cosine.
cos θ = adjacent side / hypotenuse
where θ = 39°
hypotenuse - 17 m
adjacent side - x
we need to solve for x

cos 39° = x / 17
cos 39° = 0.77
0.7771 = x/17
x = 0.7771 x 17
x = 13.21 m
distance from Roman's feet to the base of the pole is 13.21

6 0

3 years ago

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Two forces with magnitudes of 150 and 75 pounds act on an object at angles of 30° and 150°, respectively. Find the direction and

Anastaziya [24]

The problem is modelled in the first picture shown below

To work out the resultant vector, we modelled the vectors 150N and 75N as triangle AOB is shown in the second picture with AB as the resultant vector.

We use the cosine rule to work out the length AB
$AB^{2}= 75^{2}+ 150^{2}-(2*75*150*cos(60))$
$AB^{2} =28125-11250$
$AB^{2}=16875$
$AB= \sqrt{16875} =130$ (nearest whole number)

The third picture shows the full diagram of the vectors

To work out the direction of the resultant vector, we use the sin rule to find the size of angle A and angle B

Angle A
$\frac{130}{sin(60)}= \frac{75}{sin(A)}$
$130sin(A)=75sin(60)$
$sin(A)= \frac{75sin(60)}{130}$
$sin(A)=0.4996300406$
$A= sin^{-1}(0.4996300406)$
$A=30$ (rounded to nearest whole number)

Angle B
$B=180-60-30=90$

Direction is 60° toward negative x-axis

Answer: Magnitude 130N and direction 60° toward negative x-axis

3 0

3 years ago