PQ is a vertical tower having P as the foot. A,B,C are three points in the horizontal plane through P. The angles of elevation of Q from A,B,C are equal and each is equal to theta . The sides of the triangle ABC are a,b,c, and area of the triangle ABC is del . Then prove that the height of the tower is (abc) tantheta/(4)dot

Take three different colour sheets , place one over the other and draw a triangle on the top sheet. Cut the sheets to get triangles of different colour which are identical. Mark the vertices and the angles as shown. Place the interior angles angle1,angle2 and angle3 on a straight line, adjacent to each other, without leaving any gap. What can you say about the total measure of the three angles angle1,angle2 and angle3 ? Can you use the same figure to explain the ''Exterior angle property'' of a triangle ? If a side of a triangle is stretched, the exterior angle so formed is equal to the sum of the two remote interior angles.

Three equal charges, each having a magnitude of. 2.0 xx 10 ^ (-6) C , are placed at the thre corners of a right. angled triangle of sides 3 cm, 4cm and 5 cm. find the force (in magnitude) on the charge at the right angled

A 12cm wire is given a shape of a right angled triangle ABC having sides 3cm, 4cm and 5cm as shown in the figure. The resistance sides between two ends (AB, BC, CA) of the respective sides are measured one by one by a multi-meter. The resistances will be in the ratio

Step 1 : Take a chart and cut it like a triangle as shown in Fig. (a). Step 2 : Then fold it along the symmetric line AD. Then C and B will be one upon the other. Step 3 : Similarly fold it along CE, then B and A will be one upon the other. Step 4 : Similarly fold it along BF, then A and C will be one upon the other. Find AB, AC, BD, DC using a scale. Find (AB)/(AC), (BD)/(DC) check if they are equal ? In the three cases, the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the corresponding sides containing the angle. What do you conclude from this activity ?

Answer the following questions regarding earth's magnetism. a. A vector needs three quantities conventionally used to specify the earth's magnetic field. b. The angle of dip at a location in southern India is about 18^@ . Would you expect a greater or smaller dip angle in Britain ? c. If you made a map of magnetic field lines at Melboune in Australia, would the lines seem to go into the groung or come out of the ground ? d. In which direction would a compass free to move in the vertical plane point to , if located right on the geomagnetic north or south pole ? e. the earth' s field, it is claimed roughly approximates the field due to a dipole of magnetic moment 8 xx10^(22)JT^(-1) located at its centre. Check the order of magnitude of this number in some way. f. Geologists claim that besides the main magnetic N - S poles, there are several local poles on the earth's surface oriented in different directions. How is such a thing possible at all ?

Answer the following questions . a. The earth's magnetic field varies from point is space. Does it also change with time ? It so , on what time scate does it change appreciably ? b. The earth's core is known to contain iron. Yet geologists do not regard this as a source of the earth's magnetism why ? c. The charged currents in the outer conducting regions of the earth's core are thought to be responsible for earth's magnetism . What might be the ' battery ' (i.e., the source of energy) to sustain these currents ? d. The earth may have even reversed the direction of its field several times during its history of 4 to 5 billion years. How can geologists know about the earth's field in such distant past ? e. The earth's field departs from its dipole substantially at large distances (greater than about 30,000 km) what agencies may be responsible for this distortion ? f. Interstellar space has an extremely weak magnetic field of the order of 10^(-12) T, Can such a weak field be of any significant consequence ? Explain. [Note : Exercise 2 is meant mainly to arouse your curiosity . Answers to some question above are tentative or unknown . Brief answers wherever possible are given at the end . For details , you should consult a good text on geomagnetism.]

Two dice are rolled simultaneously and counts are added (i) complete the table given (ii) A student that 'there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefor, each of the them has a probability 1/11 . Do you agree with this argument? Justify your answer.

Check whether AD is bisector of angle A " of " Delta ABC in each of the following (i) AB=5 cm, AC=10 cm, BD=1.5 cm and CD=3.5 cm. (ii) AB=4 cm, AC=6 cm, BD=1.6 cm and CD=2.4 cm.

Show that the relation R defined in the set A of all triangles as R={(T _(1), T _(2))):T _(1) is similar to T _(2) } is equivalence relation. Consider three right angle triangles T_(1) with sides 3,4,5,T_(2) with sides 5,12,13 and T_(3) with sides 6,8,10. Which triangles among T_(1), T_(2) and T_(3) are related ?