Solve the right triangle.
Round your answers to the nearest tenth.

A = 43°

b = 26.8

c = 36.7

Step-by-step explanation:

✔️Find A:

A + 90° + 47° = 180° (sum of triangle theorem)

A + 137° = 180°

Subtract 137° from each side

A = 180° - 137°

A = 43°

✔️Find b and c by applying trig functions:

Reference angle = 47°

Opposite = b

Hypotenuse = c

Adjacent = 25

To find b, apply TOA:

Tan 47° = Opp/Hyp

Tan 47 = b/25

25*Tan 47 = b

26.8092178 = b

b = 26.8 (nearest tenth)

To find c, apply CAH:

Cos 47° = Adj/Hyp

Cos 47° = 25/c

c*Cos 47° = 25

c = 25/Cos 47°

c = 36.6569796

c = 36.7 (nearest tenth)

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

95.03 is the answer. hope this !