Mathematics, 24.05.2021 01:00 kashishmehta917

If cot0 =4/3 find csc0

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Answer from: Kingmoney959

$\mathrm{d. \csc \theta =\frac{5}{3}}$

Step-by-step explanation:

In a right triangle only, the tangent of an angle is equal to its opposite side divided by its adjacent side. If $\cot\theta =\frac{4}{3}$ as given in the problem, then $\tan \theta =\frac{3}{4}$ , because $\tan \theta =\frac{1}{\cot \theta}$ . Therefore, the opposite side of angle theta is 3 and its adjacent side is 4. Thus, the hypotenuse of the triangle must be $h=\sqrt{4^2+3^2}=\sqrt{25}=5$ .

The sine of an angle in a right triangle is equal to its opposite side divided by its hypotenuse.

Therefore, $\sin \theta =\frac{3}{5}$ (o/h) and since $\sin \theta =\frac{1}{\csc \theta}$ , we have:

$\csc \theta=\frac{1}{\sin \theta}=\frac{1}{\frac{3}{5}}=\boxed{\frac{5}{3}}$

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

Answer from: Quest

probably .5

i can on others if necessary.