Mathematics, 29.01.2020 12:05, Faizalcell2120

Abc is a right triangle. if ab=3 and ac=7, find bc. leave your answer in simplest radical form.

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ANSWER

$|BC| = \sqrt{58}$

EXPLANATION

Since the given triangle has a right angle, we can apply the Pythagorean Theorem to obtain,

${ |BC| }^{2} = { |AC| }^{2} + { |AB| }^{2}$
We substitute the length of the given sides to obtain,

${ |BC| }^{2} = { 7}^{2} + { 3 }^{2}$

We evaluate to obtain,

${ |BC| }^{2} = 49 + 9$

We simplify the right hand side to get,

${ |BC| }^{2} = 58$

We take the positive square root of both sides to get,

$|BC| = \sqrt{58}$

The correct answer is D.

answered: Guest

step-by-step explanation:

answered: Guest

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.