To unload hollow blocks from a cargo truck a wooden plank whose end rests against the truck’s flat-form 1.5 meters above the ground is used. If it is inclined 37 degrees 49 minutes with the ground, how long is the wooden plank?
1.5/x = sin 37°49'
so now just solve for x
Mr. Abad is beside a Santol tree S which is directly west of a Mango tree M. He walks straight to the point A 63.6 meters North, and finds that angle SMA is 51 degrees 36 minutes.
Mr. Abad is beside a Santol tree S which is directly west of a Mango tree M. He walks straight to the point A 63.6 meters North, and finds that angle SMA is 51 degrees 36 minutes.
a) What is the distance between the two trees?
b) How far is he from the Mango tree at his second position?
The Sibago Island lighthouse in Zamboanga stands on a rock 163.4 meters above sea level. A man in a vinta 151.6 meters away from the vertical axis of the light house, observes that the angle of elevation of the top of the lighthouse is 51 degrees 7 minutes. How tall is the light house?
Review your basic trig functions.
For the Mango tree,
AS/SM = tanM
AS/AM = sinM
If the lighthouse has height h, then
(163.4+h)/151.6 = tan51°7'
To find the length of the wooden plank, you can use trigonometry. The given information provides an inclined angle of 37 degrees 49 minutes and the height of the truck's platform above the ground, which is 1.5 meters.
1. First, convert the angle from degrees and minutes to decimal form. There are 60 minutes in a degree, so 49 minutes is equal to (49/60) degrees. Adding this to 37 degrees gives us a total of 37.82 degrees.
2. Now, we can use the trigonometric function tangent (tan) to find the length of the wooden plank. Because the plank is the side opposite to the angle and the height is the side adjacent to the angle, we can use the equation:
tan(angle) = opposite/adjacent
tan(37.82 degrees) = opposite/1.5 meters
Solving for the opposite side (length of the wooden plank):
opposite = tan(37.82 degrees) * 1.5 meters
3. Use a scientific calculator or a trigonometric table to find the tangent of 37.82 degrees and multiply it by 1.5 meters to get the length of the wooden plank.
opposite ≈ 1.125 meters
Therefore, the length of the wooden plank is approximately 1.125 meters.