All categories

2 years ago

In this triangle, the product of sin B and tan C is and the product of sin Cand tan B is

Mathematics

1 answer:

Ipatiy [6.2K]2 years ago

7 0

Answer:

$\frac{c}{a}$ and $\frac{b}{a}$

Step-by-step explanation:

sinB = $\frac{opposite}{hypotenuse}$ = $\frac{AC}{BC}$ = $\frac{b}{a}$

tanC = $\frac{opposite}{adjacent}$ = $\frac{AB}{AC}$ = $\frac{c}{b}$

Thus

sinB tanC = $\frac{b}{a}$ × $\frac{c}{b}$ ( cancel b on numerator/ denominator )

= $\frac{c}{a}$

---------------------------------------------------------------------------

sinC = $\frac{opposite}{hypotenuse}$ = $\frac{AB}{BC}$ = $\frac{c}{a}$

tanB = $\frac{opposite}{adjacent}$ = $\frac{AC}{AB}$ = $\frac{b}{c}$

Thus

sinC tanB = $\frac{c}{a}$ × $\frac{b}{c}$ ( cancel c on numerator/ denominator )

= $\frac{b}{a}$

You might be interested in

And question 2 is use your knowledge of central and inscribed angles to find M.

ivanzaharov [21]

Answer:

∠ RQS = 138°

Step-by-step explanation:

Since PR and PS are tangents to the circle, then

∠ QRP = ∠ QSP = 90°

The sum of the interior angles of PRQS = 360°

Subtract the sum of the interior angles from 360° for ∠ RQS

∠ RQS = 360° - (90 + 90 + 42)° = 360° - 222° = 138°

7 0

3 years ago

Use the pythagorean Theorem to prove the three sides of the triangle are the three sides of a right triangle. Show all of your w

weeeeeb [17]

Answer:

$2^{2}$ + $(2\sqrt{3}) ^{2}$ = 4 + 4 * 3 = 16 = $4^{2}$

Step-by-step explanation:

The Pythagorean Theorem states that the two shorter sides of a right triangle squared and added together will equal the longest side (hypotenuse) of the right triangle squared. The longest side of this right triangle is 4, 4 squared is 16. The two shorter sides of the right triangle are 2 and $2\sqrt{3}$ , squared individually would be 4 and 12, and added together they also equal 16. These sides are a valid input for the Pythagorean Theorem, so these three sides are the sides of a right triangle. 2 and $2\sqrt{3}$ being the legs of the right triangle, and 4 being the hypotenuse.

6 0

3 years ago

Solve using the linear combination method (show work)<br> 4 − 9 = 1 <br> −4 + 6 = −2

Scilla [17]

Did you type this incorrectly?

5 0

3 years ago

2. Solve the system of equations using the substitution method.

Dimas [21]

Answer:

x = 1

Step-by-step explanation:

2x + 3y = 20

2x + 3(10-4x) = 20

2x + 30 - 12x = 20

combine like terms

-10x + 30 = 20

-30 -30

-10x = -10

divide both sides by -10

x = 1

Hope this Helps!!!

7 0

3 years ago

Completely factored form of xy^3 – x^3y?

Zolol [24]

Answer:

xy(y - x)(y + x)

Step-by-step explanation:

take out a common factor xy from both terms

= xy(y² - x²)

y² - x² is a difference of squares and factors in general as (y - x)(y + x)

Hence

xy³ - x³y = xy(x - y)(x + y)

8 0

3 years ago