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JulijaS [17]
3 years ago
14

Given a regular square pyramid with RS = 6 and PX = 4, find the following measure. XT =

Mathematics
2 answers:
Ann [662]3 years ago
6 0

Answer:

XT=3\sqrt{2}\ units

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

Applying the Pythagoras Theorem

XT^{2}= XY^{2}+YT^{2}

In this problem we have

XY=RS/2=6/2=3\ units

YT=XY=3\ units

substitute

XT^{2}= 3^{2}+3^{2}

XT^{2}= 18

XT=\sqrt{18}\ units

Simplify

XT=3\sqrt{2}\ units

Lynna [10]3 years ago
5 0
I think its 3 sqrt of 2
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2 years ago
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Zolol [24]

Answer:

\angle\,JLF = 114^o  which agrees with option"B" of the possible answers listed

Step-by-step explanation:

Notice that in order to solve this problem  (find angle JLF) , we need to find the value of the angle defined by JLG and subtract it from 180^o, since they are supplementary angles. So we focus on such, and start by drawing the radii that connects the center of the circle (point "O") to points G and H, in order to observe the central angles that are given to us as 90^o and 138^o. (see attached image)

We put our efforts into solving the right angle triangle denoted with green borders.

Notice as well, that the triangle JOH that is formed with the two radii and the segment that joins point J to point G, is an isosceles triangle, and therefore the two angles opposite to these equal radius sides, must be equal. We see that angle JOH can be calculated by : 360^o-90^o-138^o=132^o

Therefore, the two equal acute angles in the triangle JOH should add to:

180^o-132^o=48^o resulting then in each small acute angle of measure 24^o.

Now referring to the green sided right angle triangle we can find find angle JLG, using: 180^o-24^o-90^o=66^o

Finally, the requested measure of angle JLF is obtained via: 180^o-66^o=114^o

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3 years ago
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  ↓↓↓

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