Find the value of trigonometric ratio
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Answer:
8 meters
Step-by-step explanation:
First, we can draw this out. The angle of depression represents the angle above the line from the bird and the apple, as shown. A line can be drawn from the bird to the apple as well as from the apple's height to the bird's height. A third line can be drawn connecting the line that goes straight up from the apple to the bird, forming a right triangle. We know that this is a right triangle because the purely vertical line from the apple's height to the bird's height is perpendicular to the horizontal line from the bird to the line right above the apple.
Next, we know that we are given an angle and the side adjacent to it. We want to find the length of the side opposite to the angle because that will give us the height from the bird to the apple, and adding that to the height from the apple to the ground will give us the height of the tree. In sohcahtoa, one equation that symbolizes this is tan x = opposite/adjacent, so
tan(55°) = opposite/adjacent
= opposite/4.5
multiply both sides by 4.5 to isolate opposite
tan(55°) * 4.5 = opposite
≈ 6.43
Adding this to the height of 1.5 meters from the apple to the ground, we get the height of the tree to be approximately 7.93, rounding up to 8 meters
Assume a standard deck of 52 cards with 4 suits of 13 cards each.
a. There are ways of being dealt a hand consisting of 8 hearts and 2 non-hearts, so the probability of being dealt such a hand is
b. This time, the non-hearts specifically belong to the suit of diamonds, for which there are ways of getting drawn, so the probability is