In isosceles triangle NTS, NT ≌ TS. If m∠N = 42° and NS = 30 cm, find the length of the altitude of △NTS. (Round answer to the nearest tenth.)

13.5 cm

Step-by-step explanation:

The altitude of the base of the isosceles triangle bisects the vertex angle, <T, and also bisects the base, NS.

Therefore, NS is divide into two, 15 cm each.

This means we now have two right triangles from the isosceles triangle with the following:

Reference angle = 42°

Opposite = altitude = h

Adjacent = 15 cm

To find h, apply trigonometric function, TOA:

Tan 42 = Opp/Adj

Tan 42 = h/15

15 * Tan 42 = h

h = 13.5060607 ≈ 13.5 cm (nearest tenth)

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation:

place r′ so that qr′ is parallel to the tangent.

now we get that ∠r′py=∠pr′q, where y is on the tangent, on the opposite side of p from x.

also, because of the symmetry, ∠r′py=∠qpx.

finally, note that no matter where we place r, as long as it's on the correct arc, we have ∠prq=∠pr′q.

stringing all these equalities together, we end up with ∠prq=∠qpx.

this picture will show how its going to look like.

hope this by jack monhen