A group of mountain climbers are using trigonometry to find the height of a mountain located in the Rockies. From point A, which is due west of the mountain, the angle of elevation to the top is 56 degrees. From point B, which is due east of the mountain, the angle of elevation to the top is 38 degrees. Points A and B are 9.4 km apart. Determine the height of the mountain and round to the nearest metre.
I calculated it but not sure if this is correct. 9.4/sin86 = a/sin56
9.4sin56/sin86
a= 7.81
sin38 = h/7.81
7.81sin38 = h
h = 4.81 km
so my answer is h = 4.81 km. but its asking me in meters...
Write a basic porgram to find the trigonometric ratio of sin,cos,and tan,cotagent
convert km to meter.
1km = 1,000 meters.
therefore, 4.81km = 4,810 meters
To find the height of the mountain in meters, we can convert 4.81 km to meters.
1 km = 1000 meters
So, 4.81 km = 4.81 * 1000 = 4810 meters.
Therefore, the height of the mountain is approximately 4810 meters.
To find the height of the mountain, you need to break down the problem into smaller steps. Let's go through the steps together:
Step 1: Determine the distance between the two observation points, A and B.
You correctly stated that the distance between A and B is 9.4 km. This is an important piece of information required for the calculations.
Step 2: Calculate the height of the mountain using trigonometry.
To do this, we will use the tangent function. The formula for calculating the height of the mountain, given the distance and the angles of elevation, is as follows:
height = distance * (tan(angle1) - tan(angle2))
Let's plug in the values into the formula:
distance = 9.4 km,
angle1 = 56 degrees,
angle2 = 38 degrees.
height = 9.4 km * (tan(56 degrees) - tan(38 degrees))
Now, let's calculate this using a scientific calculator or by using trigonometric tables:
height = 9.4 km * (1.4514 - 0.7813)
height = 9.4 km * 0.6701
height ≈ 6.29394 km
Step 3: Convert the height to meters.
To convert kilometers to meters, we need to multiply the height by 1000.
height in meters = 6.29394 km * 1000
height in meters ≈ 6293.94 meters
Finally, rounding to the nearest meter, the height of the mountain is approximately 6294 meters.
Hence, your calculation of h = 4.81 km is incorrect. The correct answer is h ≈ 6294 meters.