What is the tangent ratio for ∠E
2 answers:
Answer: The tangent ratio for angle E is
Step-by-step explanation: We are given to find the tangent ratio of angle E in the figure.
From the figure, we note that
the triangle DEF is a right-angled triangle, where ∠D = 90° and ∠E is an acute angle.
We know that
tangent ratio of an angle is given by the length of the perpendicular divided by the length of the base associated with that particular angle.
Now, for angle E, we have
perpendicular = DF = 6 units
and
base = DE = 8 units.
Therefore, the tangent ratio for angle E will be
Thus, the tangent ratio for angle E is
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Answer:
Ф =
Step-by-step explanation:
It is a bit difficult to input the work here, so I uploaded an image
- First we can use the trig identities to change sec²(Ф) to tan²(Ф) + 1
- Then we can combine like terms
- Then we can factor this as a polynomial function
- Then we can set each term equal to zero and solve for Ф
- The first term tan(Ф) - 2 = 0 has no solution because tan(Ф) ≠ -2 anywhere
- The second term tan(Ф) - 1 = 0 has two solutions of
and
so these are the solutions to the problem
