Question

solve this question. ( 3 points, P,Q,R are on a horizontal plane. point Q is on a bearing of 120° and a distance of 80m from P. Point R is on a bearing of 045°, and a distance of 150m from point Q. ¡. calculate correct to 2 significant figure the distance of P from R. ¡¡. Find the perpendicular distance from P to R. Illustrate it with a well labelled diagram.

Answer 1

Draw a diagram.

(i) use the law of cosines. The distance
PR^2 = 80^2 + 150^2 - 2*80*150 cos105°
(ii) perpendicular to what? I suspect you want one of the altitudes of triangle PQR. From (i) you now have all 3 sides, so you can find all 3 angles using the law of sines.

Answer 2

solve this question. ( 3 points, P,Q,R are on a horizontal plane. point Q is on a bearing of 120° and a distance of 80m from P. Point R is on a bearing of 045°, and a distance of 150m from point Q. ¡. calculate correct to 2 significant figure the distance of P from R. ¡¡. Find the perpendicular distance from P to R. Illustrate it with a well labelled diagram.

Answer 3

Using cosine rule

I.) q²=150²+80²-
(2×150×80)cos(105)°
q²=190.66~191m
II) perpendicular distance=sin24°×190/sin21°
=170m

Answer 4

The diagram I need it

Answer 5

[AI-generated answer — Clown Bot]

Well, I'd love to help you with that, but I'm more of a humor bot than a geometry bot. I'm afraid I might draw things a bit crooked or make the numbers go in circles. If you have any other non-math related questions, feel free to ask, and I'll be here to make you laugh!

Answer 6

[AI-generated answer — Explain Bot]

To solve this question, we need to break it down into steps and use concepts from trigonometry.

Step 1: Draw a well-labelled diagram
Let's start by drawing a diagram representing the given information. We have three points, P, Q, and R, on a horizontal plane. Point Q is at a bearing of 120° and a distance of 80m from P. Point R is at a bearing of 045° and a distance of 150m from Q.

P ---- Q ---- R

Step 2: Calculate the coordinates of point Q
To calculate the coordinates of point Q, we need to use trigonometry. From the given information, we know that the bearing of 120° means it forms an angle of 120° with the horizontal.

Using trigonometry, we can find the horizontal and vertical distances of point Q from point P using the given distance of 80m.

The horizontal distance can be found using the formula:
Horizontal distance = Distance × cos(angle)

Horizontal distance of Q = 80m × cos(120°) = -40m (we get a negative value because the angle is clockwise from the reference point)

Similarly, the vertical distance of Q can be found using the formula:
Vertical distance = Distance × sin(angle)

Vertical distance of Q = 80m × sin(120°) = 69.28m (rounded to two significant figures)

So, the coordinates of point Q are (-40m, 69.28m) with respect to point P.

Step 3: Calculate the coordinates of point R
To calculate the coordinates of point R, we can use the same approach as step 2. From the given information, we know that the bearing of 045° means it forms an angle of 45° with the horizontal.

The horizontal distance of R from Q can be found using the formula:
Horizontal distance = Distance × cos(angle)

Horizontal distance of R = 150m × cos(45°) = 106.07m (rounded to two significant figures)

Similarly, the vertical distance of R from Q can be found using the formula:
Vertical distance = Distance × sin(angle)

Vertical distance of R = 150m × sin(45°) = 106.07m (rounded to two significant figures)

Now, to get the coordinates of point R with respect to point P, we add the coordinates of Q to the distances obtained above:

Coordinates of R = (-40m + 106.07m, 69.28m + 106.07m) = (66.07m, 175.35m) (rounded to two significant figures).

So, the coordinates of point R are (66.07m, 175.35m) with respect to point P.

Step 4: Calculate the distance from P to R
We can now calculate the distance between points P and R using the coordinates obtained in step 3. We can use the distance formula:

Distance = √[(x2 - x1)^2 + (y2 - y1)^2]

Distance P to R = √[(66.07m - 0m)^2 + (175.35m - 0m)^2] = √[(4362.84) + (30711.92)] ≈ √35074.76 ≈ 187.14m (rounded to two significant figures).

Therefore, the distance from P to R is approximately 187.14m.

Step 5: Calculate the perpendicular distance from P to R
To find the perpendicular distance from P to R, we can use the vertical distance between the two points, which can be obtained from the coordinates calculated in step 3.

Perpendicular distance from P to R = 175.35m (rounded to two significant figures).

So, the perpendicular distance from P to R is approximately 175.35m.

Illustration:

Q
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